Answer:
6.941 grams
Explanation:
The molecular formula for Lithium is Li. The Si base unit for amount of substance is mole. 1 mole is equal to 1 moles Lithium, or 6.941 grams
Answer:
9.647989999999998
Explanation:
Assign priorities in the following set of substituents according to Cahn-Ingold-Prelog rules. -NH2 -CH2OH -OH -Br A B C D (Provide your ranking through a string like abcd, starting with the one with the highest priority. Your answer does not need to be capitalized.)
Complete Question
The complete question is shown on the first uploaded image
Answer:
[tex]-SH \ \ A[/tex]
[tex]-NH_2 \ \ B[/tex]
[tex]-COOH \ \ C[/tex]
[tex]-CH_3 \ \ D[/tex]
Explanation:
Now to correctly assign priorities in the following set of substituents we need to consider the molecular weight of the atom that is been directly attached to the carbon bond
Now an atom with a higher molecular weight will imply that the substituent will have the the highest priority
So S (32.065 u)with a the highest molecular weight implies that -SH has the highest priority
Next is N with molecular weight(14.0067 u) implies that -[tex]NH_2[/tex] will have the next priority
Next is O with molecular weight(15.999 u) implies that [tex]-COOH[/tex] will have the next priority
The Last is H with molecular weight(1.00784 u) implies that [tex]-CH_3[/tex] will have the next priority
Calculate the final temperature of 12.0 g of Argon (considered as an ideal gas) that is expanded reversibly and adiabatically from V1 = 1.00 dm3 at T1 = 273.15 K to V2 = 3.00 dm3 . CV,m(Ar) = (3/2) * R.
Answer:
Explanation:
For adiabatic change the expression is
= [tex]PV^\gamma=constant[/tex]
[tex]=(\frac{RT}{V})V^\gamma = constant[/tex]
[tex]=TV^{\gamma-1} = constant[/tex]
[tex]=T_1V_1^{\gamma-1} =[/tex][tex]=T_2V_2^{\gamma-1}[/tex]
for Argon γ = 1.67
273.15 x 1 = T₂ x [tex]3^{1.67-1}[/tex]
T₂ = 273.15 / [tex]3^{0.67}[/tex]
= 273.15/ 2.0877
= 130.83 K.
How many hydrogen atom are present in 1.53 g of water
Answer:
[tex]=1.02x10^{23} atoms\ H[/tex]
Explanation:
Hello,
In this case, for water, whose molar mass is 18 g/mol, we can find two moles of hydrogen in one mole of water, therefore, for us compute the atoms, we should also use the Avogadro's number as shown below:
[tex]=1.53gH_2O*\frac{1molH_2O}{18gH_2O}*\frac{2molH}{1molH_2O} *\frac{6.022x10^{23}atoms\ H}{1molH} \\\\=1.02x10^{23} atoms\ H[/tex]
Regards.
g + In a coffee-cup calorimeter, when 3.25 g of NaOH is dissolved in 50.00 g of water initially at 22.0 oC, the temperature of the solution increases to 24.8 oC. Calculate the q of the reaction in kJ/mol of NaOH. Assume that the specific heat of the solution is 4.184 J/g oC, and that there is no other heat transfer than that of the solution process itself.
Answer:
THE STANDARD HEAT OF SOLUTION OF SODIUM HYDROXIDE IN WATER IS -7.68 KJ PER MOLE.
Explanation:
Variables:
Mass of NaOH = 3.25 g
Mass of water = 50 g
Initial temperature of water = 22°C = 22 + 273 K = 295 K
Final temperature of the reaction mixture = 24.8 °C = 24.8 + 273 K = 297.8 K
Assuming that:
1. specific heat of water = 4.184 J/g °C
2. total mass of the reaction mixture = 50 g + 3.25 g = 53.25 g
3. the rise in temperature = (297.8 K - 295 K ) = 2.8 K
4. Molar mass of sodium hydroxide = ( 23 + 16 + 1) = 40 g/mol
5. number of mole of sodium hydroxide = mass / molar mass
n = 3.25 g / 40 g/mol
n = 0.08125 moles
The rise in temperature for the reaction mixture produces how much of heat:
Heat = mass * specific heat * change in temperature
Heat = 53.25 * 4.184 * 2.8
Heat = 623.8344 J of heat.
Equation of reaction:
NaOH + H2O -------> NaOH + H2O + Heat
This is not a reaction but a dissolution as sodium hydroxide is very soluble in water and this reaction is exothermic where heat is given off.
So since 3.25 g having 0.08125 moles produces 623.8344 J of heat, 1 mole of the sodium hydroxide used will produce:
0.08125 mole of sodium hydroxide = 623.8344 J of heat
1 mole of sodium hydroxide = ( 623.8344 / 0.08125 J of heat
= 7677.96 J of heat per mole of sodium hydroxide.
= 7.68 kJ of heat
So therefore, the standard heat of solution of sodium hydroxide in water is -7.68 kJ of heat since its an exothermic reaction.
If you made a three-dimensional model of an atom and its nucleus, how would you represent the atom? 7th grade
Answer:
it shows the breakdown of the atom
Explanation:
it will show it molecularly
which of the following objects have kinetic energy? check all that apply
Answer:
what are the options?
Explanation:
do you have multiple choice for this question?
Answer:
A book inside a vehicle, a running cat, and a falling meteorite.
Explanation:
I just took it
Sort The following iron compound by whether the cation is iron(II) or iron(III)
Answer:
Left, Left, Right, Left, Right, Right
Explanation:
Follow that order!
g 1. An ideal gas is confined to a container with adjustable volume. The number of moles, n, and temperature, T, are constant. By what factor will the volume change if pressure decreases by a factor of 8.5 Hint: pV
Answer:
The volume will increase by a factor of 8.5
Explanation:
In an ideal gas, the volume is inversely proportional to the pressure. This means that the volume will decrease when the pressure increases and vice versa.
Let the initial volume be v1, and the initial pressure p1.
the final pressure is decreased by a factor of 8.5, i.e
p2 = p1/8.5 = 0.12p1
using p1v1 = p2v2
v2 = (p1/p2)v1
v2 = (p1/0.12p1)v1
v2 = 8.5v1
This means that the final pressure increases by a factor of 8.5
Answer:
Increases by a factor of 8.5
Explanation:
Hello,
In this case, with the given data, we can apply the Boyle's law in order to understand the pressure-volume behavior as an inversely proportional relationship:
[tex]P_1V_1=P_2V_2[/tex]
Thus, for the given pressure decrease we have:
[tex]P_2=\frac{P_1}{8.5}[/tex]
So the volume changes by:
[tex]V_2=\frac{P_1V_1}{\frac{P_1}{8.5} } \\\\V_2=8.5V_1[/tex]
Therefore, it increases by a factor of 8.5.
Regards.
A sample of copper absorbs 4.31E+1 kJ of heat, resulting in a temperature rise of 6.71E+1 °C. Determine the mass (in kg) of the copper sample if the specific heat capacity of copper is 0.385 J/g°C.
Answer: 1.67 kg
Explanation:
The quantity of heat required to raise the temperature of a substance by one degree Celsius is called the specific heat capacity.
[tex]Q=m\times c\times \Delta T[/tex]
Q = Heat absorbed=[tex]4.31\times 10^1kJ[/tex] = [tex]43100J[/tex] (1kJ=1000J)
m= mass of substance = ?
c = specific heat capacity = [tex]0.385J/g^0C[/tex]
Change in temperature ,[tex]\Delta T=T_f-T_i=6.71\times 10^1^0C=67.1^0C[/tex]
Putting in the values, we get:
[tex]43100J=m\times 0.385J/g^0C\times 67.1^0C[/tex]
[tex]m=1670g=1.67kg[/tex] (1kg=1000g)
Thus the mass (in kg) of the copper sample is 1.67
(i) 1s 2 2s 2 2p 6 3s 1 (ii) 1s 2 2s 2 2p 6 3s 2 (iii) 1s 2 2s 2 2p 6 3s 2 3p 1 (iv) 1s 2 2s 2 2p 6 3s 2 3p 4 (v) 1s 2 2s 2 2p 6 3s 2 3p 5 The electron configuration of the atom that is expected to have a positive electron affinity is ________.
Answer:
(V) 1s 2 2s 2 2p 6 3s 2 3p 5
Explanation:
Electron Affinity can be defined as the energy associated with a neutral atom, when an electron is added to form a negative ion.
1s 2 2s 2 2p 6 3s 2 3p 5 , is the electronic configuration of Chlorine.
The electron affinity is positive because it is an exorthermic reaction, meaning that, energy was released during the addition of an electron to the atom.
Cl (g) + e- -------> Cl- (g) = -349KJ/mol
which statement best describle for formation of solution
Explanation:
small amount of solute is dissolved in a large amount of solvent. it would not make sense to have more solute and solvent. you can think of it like this, you can dissolve a teaspoon of salt in a litre water but you can't resolve 1 kg of salt in a teaspoon of water.
also, the solute is what is begin dissolved and the solvent is what dissolving the solute so the one day the solvent is dissolved in the solute does not make complete sense.
Suppose there is 0.63 g of HNO3 per 100 mL of a particular solution. What is the concentration of the HNO3 solution in moles per liter?
Answer:
There are 0.09996826 moles per liter of the solution.
Explanation:
Molar mass of HNO3: 63.02
Convert grams to moles
0.63 grams/ 63.02= 0.009996826
Convert mL to L and place under moles (mol/L)
100mL=0.1 L
0.009996826/0.1= 0.09996826 mol/L
The concentration of the HNO₃ solution is 10⁻¹ moles per liter.
What is Molar Concentration ?
Molar Concentration is known as Molarity. It is the number of moles of solute present in per liter of the solution.
Molar concentration in terms of Molecular weight
C = [tex]\frac{m}{V} \times \frac{1}{M.W}[/tex]
where,
C is the molar concentration in mol/L
m is the mass or weight of solute in grams
V is volume of solution in liters
M.W is the molecular weight in g/mol
Molar concentration of HNO₃ = [tex]\frac{\text{Mass of}\ HNO_3}{\text{Liter of solution}} \times \frac{1}{\text{Molecular weight of}\ HNO_3}[/tex]
Molecular weight of HNO₃ = Atomic weight of H + Atomic weight of N + 3 (Atomic weight of O)
= 1 + 14 + 3 (16)
= 15 + 48
= 63 g/mol
Convert mL into L
1 mL = 0.001 L
100 mL = 100 × 0.001
= 0.1 L
Now, put the value in above formula we get
Molar concentration of HNO₃ = [tex]\frac{\text{Mass of}\ HNO_3 / \text{Liter of solution}}{\text{Molar mass of}\ HNO_3}[/tex]
= [tex]\frac{0.63\ g / 0.1\ L}{63\ g/mol}[/tex]
= [tex]\frac{6.3}{63}[/tex]
= 0.1
= 10⁻¹ moles per liter
Thus, we can say that 10⁻¹ moles per liter is the concentration of the HNO₃ solution.
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The conversion of methyl isonitrile to acetonitrile in the gas phase at 250 °C CH3CN(g) is first order in CH3NC with a rate constant of 3.00×10^-3 s-1. If the initial concentration of CH3NC is 5.45×10^-2 M, the concentration of CH3NC will be 1.56×10^-2 M after_____________ s have passed.
Answer: The concentration of [tex]CH_3NC[/tex] will be [tex]1.56\times 10^{-2}M[/tex] after 416 seconds have passed.
Explanation:
Expression for rate law for first order kinetics is given by:
[tex]t=\frac{2.303}{k}\log\frac{a}{a-x}[/tex]
where,
k = rate constant = [tex]3.00\times 10^{-3}s^{-1}[/tex]
t = age of sample = ?
a = let initial amount of the reactant = [tex]5.45\times 10^{-2}M[/tex]
a - x = amount left after decay process = [tex]1.56\times 10^{-2}M[/tex]
[tex]t=\frac{2.303}{3.00\times 10^{-3}}\log\frac{5.45\times 10^{-2}}{1.56\times 10^{-2}}[/tex]
[tex]t=416s[/tex]
The concentration of [tex]CH_3NC[/tex] will be [tex]1.56\times 10^{-2}M[/tex] after 416 seconds have passed.
if two atoms are bonded to a central atom with no lone pairs , how will they be arranged?
A salt contains a compound containing a metal and a nonmetal. This is an
compound. *
A.molecular
B.covalent
C.Tonic
D.None of the above
Answer:
Option C. Ionic
Explanation:
Ionic bond is formed between a metal and a non metal.
Ionic bond occurs when there is a transfer of electron(s) from a metallic atom to a non metallic atom.
Write the identity of the missing nucleus for the following nuclear decay reaction:
232 Th 228Ra+?
90
88
low.
Express your answer as a particle.
View Available Hints
Hint 1. Determine the missing mass number
1
Hint 2. Determine the missing atomic number
Hint 3. Determine the symbol of the new nucleus
?
Answer:
Alpha decay: 4 2He
Explanation:
Considering the equation given in the question, we can see that the mass number of daughter nuclei (228 88Ra) reduce by 4 and the atomic number reduce by 2 when compared with the parent nucleus (232 90Th). This simply indicates that the parent nucleus is undergoing alpha decay.
Therefore, the missing nucleus is
4 2He i.e alpha decay.
Please see attachment photo for further details.
Complete the sentence indicating the number of protons and electrons in the given ion. Match the numbers in the left column to the appropriate blanks in the sentences on the right. The ion P3− has The ion P 3 − has blank protons and blank electrons. protons and The ion P 3 − has blank protons and blank electrons. electrons.
What isotope has 17 protons and 18 neutrons? Enter the name of the element followed by a hyphen and the mass number (e.g., uranium-234).
Which element does X represent in the following expression: 4120X? Enter the chemical symbol of the element. X is the element symbol . Provide Feedback Correct. Followup. All bromine atoms have 35 protons. A neutral atom also has 35 electrons. The sum of the protons and neutrons gives the mass number, . End of followup.
Answer: (Chlorine-35)
Element X is Ca
Explanation:
Number of proton plus the number of electron gives the mass number.
write briefly how oxygen gas is prepared in the industry
by fractional distillation of liquefied air or the use of zeolites to remove carbon dioxide and nitrogen from air or the electrolysis of water
Many computer chips are manufactured from silicon , which occurs in nature as SiO2. WhenSiO 2 is heated to melting , it reacts with solid carbon to form liquid silicon and carbon monoxide gas. In an industrial preparation of silicon, 155.8 kg of SiO2 reacts with 78.3 kg of carbon to produce 66.1 kg of silicon. Determine the limiting reactant, theoretical yield, and percent yield for the reaction.
Answer:
In the given case, SiO2 is the limiting reactant, 71.72 Kg is the theoretical yield, and 90.8 percent is the experimental yield.
Explanation:
A reactant that completely gets used up in a chemical reaction, and it limits the concentration of product, which can be produced is termed as a limiting reactant. The maximum concentration of product that can get generated from the limiting reactant is termed as the theoretical yield.
Based on the given question, the balanced chemical reaction is:
SiO₂ + 2C ⇒ Si + 2CO
Now the mole ratio of SiO₂: C = 1: 2
Based on the given information, the mass of SiO₂ is 155.8 Kg. The no. of moles can be calculated by using the formula, n = weight/molecular mass.
The molecular mass of SiO₂ is 60.08 gram per mole. By putting the values we get,
n = 155.8 × 10³ grams / 60.08 grams/mol
n = 2.59 × 10³ moles
The weight of Carbon given is 78.3 Kg or 78.3 × 10³ grams, the molecular mass of C is 12 gram per mole. Similarly, the moles of C will be,
n = 78.3 × 10³ grams / 12 g/mol
n = 6.52 × 10³ moles
The experimental molar ratio of SiO₂: C is,
= 2.59 × 10³: 6.52 × 10³
= 2.59: 6.52 = 1: 2.5
Hence, it is clear that carbon in the given case is present in excess amount, therefore, SiO₂ is a limiting reactant.
With the help of the balanced equation, the molar ratio of SiO₂: Si is 1: 1. As SiO₂ is the limiting reactant, therefore, theoretical yield of the reaction will be determined by SiO₂.
As calculated, the moles of SiO₂ used is 2.59 × 10³
Hence, the moles of Si produced in the given reaction is 2.59 × 10³.
Now the mass of Si produced theoretically can be determined by using the formula, moles = weight/molar mass. The molar mass of Si is 28.08 gram per mole. Now putting the values we get,
Weight = 2.59 × 10³ moles × 28.08 gram per mole
Weight = 72.72 × 10³ grams or 72.72 Kg
The theoretical yield of Si is 72.72 Kg, however, the experimental yield is 66.1 Kg. Therefore, the percent yield for the reaction will be,
= Experimental yield / Theoretical yield × 100 %
= 66.1 Kg / 72.72 Kg × 100%
= 90.8 %
The H 2 produced in a chemical reaction is collected through water in a eudiometer. If the pressure in the eudiometer is 760.0 torr and the vapor pressure of water under the experimental conditions is 23.8 torr, what is the pressure (torr) of the H 2 gas
Answer:
the pressure (torr) of theH₂ gas is 736.2 torr
Explanation:
Given that
The H₂ gas produced in a chemical reaction is collected through water in a eudiometer; during this process, the gas collected contains some droplets of water vapor along with these gas.
So; the total pressure in the eudiometer = Pressure in the H₂ gas - Pressure of the water vapor
Where;
[tex]P_{Totsl}[/tex] = total pressure in the eudiometer = 760.0 torr
[tex]P_{H_2}[/tex] = Pressure in the H₂ gas = ???
[tex]P_{H_2O}[/tex] = Pressure in the water vapor = 23.8 torr
Now:
[tex]P_{Totsl}[/tex] = [tex]P_{H_2}[/tex] + [tex]P_{H_2O}[/tex]
- [tex]P_{H_2}[/tex] = + [tex]P_{H_2O}[/tex] - [tex]P_{Totsl}[/tex]
[tex]P_{H_2}[/tex] = - [tex]P_{H_2O}[/tex] + [tex]P_{Totsl}[/tex]
[tex]P_{H_2}[/tex] = (- 23.8 + 760) torr
[tex]P_{H_2}[/tex] = 736.2 torr
Thus; the pressure (torr) of theH₂ gas is 736.2 torr
If the pressure in a eudiometer is 760.0 torr and the vapor pressure of water is 23.8 torr, the pressure of the H₂ gas is 736.2 torr.
A eudiometer is a laboratory device that measures the change in volume of a gas mixture following a physical or chemical change. Usually, the gas is collected over water.
According to Dalton's law of partial pressures, the sum of the sum partial pressure of the hydrogen and the partial pressure of the water is equal to the total pressure in the eudiometer.
[tex]P = pH_2 + pH_2O\\\\pH_2 = P - pH_2O = 760.0 torr - 23.8 torr = 736.2 torr[/tex]
If the pressure in a eudiometer is 760.0 torr and the vapor pressure of water is 23.8 torr, the pressure of the H₂ gas is 736.2 torr.
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4. Alex is a soil specialist and he sells manure best suited for wheat. He goes to a village where farmers are
planning to sow wheat which grows best in clayey and loamy soil. He tests the soil sample and finds
that the soil is more suitable for the growth of cotton rather than wheat. He tells the villagers about
this despite knowing that they will not buy his manure.
(a) Why is clayey-loamy soil preferred for growing wheat?
(b) Which value is shown by Alex?
Please answer the question fast
Answer:
Explanation:
1) Clayey-loamy soil tends to be excellent at retaining water which is critical for proper growth of wheat thus this kind of soil is preferred.
2) Alex is showing honesty as he informing the villagers about the actual truth and reality (he is not basing his answers on judgements rather he is basing it on scientific knowledge and being honest about it)
A substance is considered to have a smaller surface area when...
A. it is a fine powder
B. it is in large chunks
C. you have a small amount of
the substance
D. you have a large amount of E. the substance
Can the pH scale be utilized for all acids (Arrhenius, Bronsted-Lowery, and Lewis)? Give examples of substances from each definition category that can/cannot use the pH scale and explain your reasoning.
Explanation:
Before proceeding to answering the questions, let us go over some definitions.
pH scale: The pH scale measures how acidic or basic a substance is. The pH scale ranges from 0 to 14. A pH of 7 is neutral. A pH less than 7 is acidic.
pH stands for Potential of Hydrogen. It refers to the hydrogen ion concentration in a solution.
The keywords being; Hydrogen Ion concentration.
A Bronsted-Lowry acid is a chemical species that donates one or more hydrogen ions in a reaction.
A Lewis acid is any substance that can accept a pair of nonbonding electrons. It is an electron pair acceptor.
An Arrhenius acid is a substance that dissociates in water to form hydrogen ions or protons.
Based on the definitions of given above, it is obseved that both Bronsted lowry and arrhenius acids deals with hydrogen ions. Hence both of this acids can be measured using the pH scale. The lewis acid on the other hand do not necessarily contain hydrogen ions, hence the pH scale cannot be utilized for it.
Examples includes;
Arrhenius acid; Nitric Acid – HNO3 etc
Lewis acid; boron trifluoride (BF3) and aluminum fluoride (AlF3) etc
Bronsted lowry acid; HCl etc
How sensitive to changes in water temperature are coral reefs? To find out, measure the growth of corals in aquariums where the water temperature is controlled at different levels. Growth is measured by weighing the coral before and after the experiment.
(a) What are the explanatory and response variables?
explanatory variable:
response variable:
(b) Are they quantitative or categorical?
The explanatory variable is:
The response variable is:
Answers:
(a) The explanatory variable is the change in the temperature .
The response variable is the coral survivance.
(b) The explanatory variable is quantitative.
The response variable is categorical.
Explanation:
A quantitative variable is those that can take a range of values. In this case, the temperature may vary across a range of values associated with the survival of coral reefs.
A categorical (also known as qualitative) variable is characterized to present finite states. In this case, the coral reefs can survive or not depending on their responses to changes in the temperature.
Response and explanatory variables are used in experimental procedure ; the explanatory and response variables are :
Measured variable - > Change in weight of coral (quantitative) Explanatory variable - > Temperature of water. (categorical)Explanatory variables are independent variables which causes changes to the measured variable.
Measured variable is the variable we intend to measure in an experiment. They are called dependent variables.
Quantitative variables are numerical values, weight is measured as a number. Hence, it is quantitative.
Categorical variables are labels and are used to group objects into classes. They are Non-numeric. Levels of temperature could be (high, medium, low). Hence, temperature is categorical in the experiment.
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Consider an Al-4% Si alloy. Determine (a) if the alloy is hypoeutectic or hypereutectic, (b) the composition of the first solid to form during solidification, (c) the amounts and compositions of each phase at 578˚C, (d) the amounts and compositions of each phase at 576˚C, (e) the amounts and compositions of each microconstituent at 576˚C, and (f) the amounts and compositions of each phase at 25˚C.
Answer:
(a) Hypoeutectic
(b) Alpha solid, aluminium
(c) 70% α , 30% β
(d) 97.6% α, 2.4% β
(e) 97.6% α, 2.4% β
(f) 97% α, 3% β
Explanation:
(a) The eutectic composition for Al Si alloy is 11.7 wt% silicon, therefore, an Al-4% Si alloy is hypoeutectic
(b) For the hypoeutectic alloy, aluminium, Al, is expected to form first, such that the aluminium content is reduced till the point it gets to the eutectic proportion of 11.7 wt% silicon
(c) At 578°C we have
% α: Al (11 - 4)/(11 - 1) = 70% α
% L: Si 100 - 70 = 30% β
(d) At 576°C we have
α: 99.83% Si (99.83 - 4)/(99.83- 1.65) = 97.6% α
β: 1.65% Si (4 - 1.65)/(99.83- 1.65) = 2.4% β
(e) Primary α: 1.65% α (99.83 - 4)/(99.83 - 1.65) = 97.6% α
Eutectic 4% Si = 100 - 97.6 = 2.4% β
(f) At 25°C we have;
α%: (99.83 - 4)/(99.83 - 1) = 97% α
β%: 100 - 97 = 3% β.
What is the color of litmus solution in sodium hydroxide?
Answer:
Sodium Hydroxide turns blue litmus red .
which two compounds are structural isomers of each other
Answer:
Explanation:
Structural isomer is a type of isomer in which molecules with the same molecular formula have different bonding patterns and atomic organization.
For example Pentan-1-ol, pentan-2-ol, and pentan-3-ol are structural isomers that exhibit position isomerism.
Cyclohexane and hex-1-ene are examples of functional group structural isomers.
3. The exosphere is the outer layer of the
O D. thermosphere
OC. mesosphere
O A. ozone layer
O B. troposhpere
ang
AT
HHH
Answer:
D. exosphere is the outer layer of the thermosphere
What is mass per unit volume called?
Answer:
The correct answer is Density
Explanation:
Hope this helps you
Answer:density
Explanation:
Two chemicals A and B are combined to form a chemical C. The rate, or velocity, of the reaction is proportional to the product of the instantaneous amounts of A and B not converted to chemical C. Initially, there are 40 grams of A and 50 grams of B, and for each gram of B, 2 grams of A is used. It is observed that 25 grams of C is formed in 8 minutes. How much (in grams) is formed in 16 minutes
Answer: 45. 78 g is formed in 16 minutes.
Explanation:
Let [tex]A_{o} =40 g[/tex] and [tex]B_{o} =50 g[/tex]
we know that [tex]\alpha =A_{o}\frac{M+N}{M}\, and \, \beta =B_{o}\frac{M+N}{N}[/tex]
According to the question to create [tex]x[/tex] part of the chemical C we will need 2 part of A and one part of B.
Therefore, M = 2 and N = 1.
Now, we can easily solve for the value of α and β.
[tex]\alpha =40\frac{2+1}{2}=60\\\\\, and \, \beta =50\frac{2+1}{1}=150[/tex]
Now, the differential equation must be: [tex]\frac{dX}{dt}=k\left ( \alpha -X \right )\left ( \beta -X \right )[/tex]
I separate the variable and solve the equation
[tex]\int \frac{dx}{\left ( 60-x \right )\left ( 150-x \right )}=\int k\, dt[/tex]
[tex]ln\frac{150-x}{60-x}=90kt+C_{1}[/tex]
By using [tex]X(0) =0[/tex],
[tex]\frac{150-x}{60-x}=Ce^{90k_{o}},C=\frac{5}{2}[/tex]
and using [tex]X (8)=25[/tex] and solving for the value of 'k'
[tex]\Rightarrow \frac{150-25}{60-25}=\frac{5}{2}e^{450k}\\\\\Rightarrow 3.6\times \frac{2}{5}=e^{450k}\\\\\Rightarrow 1.4=e^{450k}[/tex]
Taking 'ln' both side, we get
[tex]\Rightarrow k=7.4716\times 10^{-4}[/tex]
We obtain:[tex]X(t)=\frac{60Ce^{90kt}-150}{Ce^{90kt}-1}[/tex]
Now, for the 16 min
[tex]\Rightarrow X(16)=\frac{150e^{1.07559}-150}{2.5e^{1.0759}-1}[/tex]
[tex]\Rightarrow X(16)=\frac{439.7583-150}{7.3293-1}\\\\\Rightarrow X(16)=\frac{289.7583}{6.3293}[/tex]
[tex]\Rightarrow X(16)=45.78 g[/tex]
