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Reil [10]
3 years ago
11

Determine the rate law, including the values of the orders and rate law constant, for the following reaction using the experimen

tal data provided. (4 points)
A + B yieldsproducts

Trial

[A]

[B]

Rate

1 0.10 M 0.20 M 1.2 × 10-2 M/min
2 0.10 M 0.40 M 4.8 × 10-2 M/min
3 0.20 M 0.40 M 9.6 × 10-2 M/min
Chemistry
1 answer:
olga55 [171]3 years ago
6 0

Answer: Rate law=k[A]^1[B]^2, order with respect to A is 1, order with respect to B is 2 and total order is 3. Rate law constant is 3L^2mol^{-2}s^{-1}

Explanation: Rate law says that rate of a reaction is directly proportional to the concentration of the reactants each raised to a stoichiometric coefficient determined experimentally called as order.

Rate=k[A]^x[B]^y

k= rate constant

x = order with respect to A

y = order with respect to A

n = x+y = Total order

a) From trial 1: 1.2\times 10^{-2}=k[0.10]^x[0.20]^y    (1)

From trial 2: 4.8\times 10^{-2}=k[0.10]^x[0.40]^y    (2)

Dividing 2 by 1 :\frac{4.8\times 10^{-2}}{1.2\times 10^{-2}}=\frac{k[0.10]^x[0.40]^y}{k[0.10]^x[0.20]^y}

4=2^y,2^2=2^y therefore y=2.

b) From trial 2: 4.8\times 10^{-2}=k[0.10]^x[0.40]^y    (3)

From trial 3: 9.6\times 10^{-2}=k[0.20]^x[0.40]^y   (4)

Dividing 4 by 3:\frac{9.6\times 10^{-2}}{4.8\times 10^{-2}}=\frac{k[0.20]^x[0.40]^y}{k[0.10]^x[0.40]^y}

2=2^x,2=2^1, x=1

Thus rate law is Rate=k[A]^1[B]^2

Thus order with respect to A is 1 , order with respect to B is 2 and total order is 1+2=3.

c) For calculating k:

Using trial 1:  1.2\times 10^{-2}=k[0.10]^1[0.20]^2

k=3 L^2mol^{-2}s^{-1}.



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<u>For 1:</u> The partial pressure of helium is 376 mmHg and that of methane gas is 445 mmHg

<u>For 2:</u> The mole fraction of nitrogen gas is 0.392 and that of carbon dioxide gas is 0.608

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<u>For 1:</u>

To calculate the number of moles, we use the equation:

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  • <u>For helium:</u>

Given mass of helium = 0.723 g

Molar mass of helium = 4 g/mol

Putting values in equation 1, we get:

\text{Moles of helium}=\frac{0.723g}{4g/mol}=0.181mol

  • <u>For methane gas:</u>

Given mass of methane gas = 3.43 g

Molar mass of methane gas = 16 g/mol

Putting values in equation 1, we get:

\text{Moles of methane gas}=\frac{3.43g}{16g/mol}=0.214mol

To calculate the mole fraction , we use the equation:

\chi_A=\frac{n_A}{n_A+n_B}     .......(2)

To calculate the partial pressure of gas, we use the equation given by Raoult's law, which is:

p_{A}=p_T\times \chi_{A}       ......(3)

  • <u>For Helium gas:</u>

We are given:

n_{He}=0.181mol\\n_{CH_4}=0.214mol

Putting values in equation 2, we get:

\chi_{He}=\frac{0.181}{0.181+0.214}=0.458

Calculating the partial pressure by using equation 3, we get:

p_T=821mmHg\\\\\chi_{He}=0.458

Putting values in equation 3, we get:

p_{He}=0.458\times 821mmHg=376mmHg

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We are given:

n_{He}=0.181mol\\n_{CH_4}=0.214mol

Putting values in equation 2, we get:

\chi_{CH_4}=\frac{0.214}{0.181+0.214}=0.542

Calculating the partial pressure by using equation 3, we get:

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Putting values in equation 3, we get:

p_{CH_4}=0.542\times 821mmHg=445mmHg

Hence, the partial pressure of helium is 376 mmHg and that of methane gas is 445 mmHg

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We are given:

Partial pressure of nitrogen gas = 363 mmHg

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<u>For nitrogen gas:</u>

363=\chi_{N_2}\times 927\\\\\chi_{N_2}=\frac{363}{927}=0.392

<u>For carbon dioxide gas:</u>

564=\chi_{CO_2}\times 927\\\\\chi_{CO_2}=\frac{564}{927}=0.608

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