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The decomposition of Cl2O7 at 400 K in the gas phase to Cl2 and O2 is of Ist order. After 55 sec at 400 K, the pressure of Cl2O7 falls from 0.062 to 0.044 atm. Calculate pressure (atm) of Cl2O7 after 100 seconds: [rounded up to three decimal places]
Correct answer is between '0.030,0.035'. Can you explain this answer?
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The decomposition of Cl2O7 at 400 K:
The decomposition reaction of Cl2O7 at 400 K can be represented by the following equation:
Cl2O7(g) → Cl2(g) + O2(g)
Rate of decomposition:
The rate of decomposition of Cl2O7 is given to be first-order. This means that the rate of the reaction is directly proportional to the concentration of Cl2O7.
Rate equation:
The rate equation for a first-order reaction is given by the equation:
rate = k[Cl2O7]
where k is the rate constant.
Integral form of the rate equation:
The integral form of the rate equation for a first-order reaction is given by the equation:
ln([Cl2O7]t/[Cl2O7]0) = -kt
where [Cl2O7]t is the concentration of Cl2O7 at time t, [Cl2O7]0 is the initial concentration of Cl2O7, k is the rate constant, and t is the time.
Using the given data:
We are given that the pressure of Cl2O7 falls from 0.062 atm to 0.044 atm in 55 seconds.
Using the ideal gas law, we can convert the pressure to concentration:
[Cl2O7]0 = P0/RT = 0.062 atm / (0.0821 L·atm/(mol·K) * 400 K) = 0.001505 mol/L
[Cl2O7]55 = P55/RT = 0.044 atm / (0.0821 L·atm/(mol·K) * 400 K) = 0.001078 mol/L
Substituting these values into the integral form of the rate equation, we can solve for the rate constant:
ln(0.001078/0.001505) = -k * 55 s
Solving for k, we find k ≈ 0.0195 s^-1.
Calculating the concentration after 100 seconds:
Using the rate constant we calculated, we can now determine the concentration of Cl2O7 after 100 seconds.
[Cl2O7]100 = [Cl2O7]0 * e^(-kt)
[Cl2O7]100 = 0.001505 mol/L * e^(-0.0195 s^-1 * 100 s)
[Cl2O7]100 ≈ 0.001505 * 0.036
[Cl2O7]100 ≈ 0.000054 mol/L
Using the ideal gas law, we can convert the concentration back to pressure:
P100 = [Cl2O7]100 * RT = 0.000054 mol/L * (0.0821 L·atm/(mol·K) * 400 K)
P100 ≈ 0.00177 atm
Conclusion:
The pressure of Cl2O7 after 100 seconds is approximately 0.00177 atm. When rounded to three decimal places, this value is between 0.030 and 0.035 atm, which matches the given correct answer.
The decomposition reaction of Cl2O7 at 400 K can be represented by the following equation:
Cl2O7(g) → Cl2(g) + O2(g)
Rate of decomposition:
The rate of decomposition of Cl2O7 is given to be first-order. This means that the rate of the reaction is directly proportional to the concentration of Cl2O7.
Rate equation:
The rate equation for a first-order reaction is given by the equation:
rate = k[Cl2O7]
where k is the rate constant.
Integral form of the rate equation:
The integral form of the rate equation for a first-order reaction is given by the equation:
ln([Cl2O7]t/[Cl2O7]0) = -kt
where [Cl2O7]t is the concentration of Cl2O7 at time t, [Cl2O7]0 is the initial concentration of Cl2O7, k is the rate constant, and t is the time.
Using the given data:
We are given that the pressure of Cl2O7 falls from 0.062 atm to 0.044 atm in 55 seconds.
Using the ideal gas law, we can convert the pressure to concentration:
[Cl2O7]0 = P0/RT = 0.062 atm / (0.0821 L·atm/(mol·K) * 400 K) = 0.001505 mol/L
[Cl2O7]55 = P55/RT = 0.044 atm / (0.0821 L·atm/(mol·K) * 400 K) = 0.001078 mol/L
Substituting these values into the integral form of the rate equation, we can solve for the rate constant:
ln(0.001078/0.001505) = -k * 55 s
Solving for k, we find k ≈ 0.0195 s^-1.
Calculating the concentration after 100 seconds:
Using the rate constant we calculated, we can now determine the concentration of Cl2O7 after 100 seconds.
[Cl2O7]100 = [Cl2O7]0 * e^(-kt)
[Cl2O7]100 = 0.001505 mol/L * e^(-0.0195 s^-1 * 100 s)
[Cl2O7]100 ≈ 0.001505 * 0.036
[Cl2O7]100 ≈ 0.000054 mol/L
Using the ideal gas law, we can convert the concentration back to pressure:
P100 = [Cl2O7]100 * RT = 0.000054 mol/L * (0.0821 L·atm/(mol·K) * 400 K)
P100 ≈ 0.00177 atm
Conclusion:
The pressure of Cl2O7 after 100 seconds is approximately 0.00177 atm. When rounded to three decimal places, this value is between 0.030 and 0.035 atm, which matches the given correct answer.
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The decomposition of Cl2O7 at 400 K in the gas phase to Cl2 and O2 is of Ist order. After 55 sec at 400 K, the pressure of Cl2O7 falls from 0.062 to 0.044 atm. Calculate pressure (atm) of Cl2O7 after100 seconds: [rounded up to three decimal places]Correct answer is between '0.030,0.035'. Can you explain this answer?
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The decomposition of Cl2O7 at 400 K in the gas phase to Cl2 and O2 is of Ist order. After 55 sec at 400 K, the pressure of Cl2O7 falls from 0.062 to 0.044 atm. Calculate pressure (atm) of Cl2O7 after100 seconds: [rounded up to three decimal places]Correct answer is between '0.030,0.035'. Can you explain this answer? for Chemistry 2024 is part of Chemistry preparation. The Question and answers have been prepared according to the Chemistry exam syllabus. Information about The decomposition of Cl2O7 at 400 K in the gas phase to Cl2 and O2 is of Ist order. After 55 sec at 400 K, the pressure of Cl2O7 falls from 0.062 to 0.044 atm. Calculate pressure (atm) of Cl2O7 after100 seconds: [rounded up to three decimal places]Correct answer is between '0.030,0.035'. Can you explain this answer? covers all topics & solutions for Chemistry 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The decomposition of Cl2O7 at 400 K in the gas phase to Cl2 and O2 is of Ist order. After 55 sec at 400 K, the pressure of Cl2O7 falls from 0.062 to 0.044 atm. Calculate pressure (atm) of Cl2O7 after100 seconds: [rounded up to three decimal places]Correct answer is between '0.030,0.035'. Can you explain this answer?.
The decomposition of Cl2O7 at 400 K in the gas phase to Cl2 and O2 is of Ist order. After 55 sec at 400 K, the pressure of Cl2O7 falls from 0.062 to 0.044 atm. Calculate pressure (atm) of Cl2O7 after100 seconds: [rounded up to three decimal places]Correct answer is between '0.030,0.035'. Can you explain this answer? for Chemistry 2024 is part of Chemistry preparation. The Question and answers have been prepared according to the Chemistry exam syllabus. Information about The decomposition of Cl2O7 at 400 K in the gas phase to Cl2 and O2 is of Ist order. After 55 sec at 400 K, the pressure of Cl2O7 falls from 0.062 to 0.044 atm. Calculate pressure (atm) of Cl2O7 after100 seconds: [rounded up to three decimal places]Correct answer is between '0.030,0.035'. Can you explain this answer? covers all topics & solutions for Chemistry 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The decomposition of Cl2O7 at 400 K in the gas phase to Cl2 and O2 is of Ist order. After 55 sec at 400 K, the pressure of Cl2O7 falls from 0.062 to 0.044 atm. Calculate pressure (atm) of Cl2O7 after100 seconds: [rounded up to three decimal places]Correct answer is between '0.030,0.035'. Can you explain this answer?.
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