Acetaldehyde, CH3CHO, will decompose into methane and carbon monoxide according to
CH3CHO (g) -> CH4 (g) + CO (g)
At 450C the rate of consumption of CH3CHO is measured to vary with the concetration of CH3CHO raised to the power 1.5.
With a CH3CHO concentration of 0.222M, the rate of consumption of CH3CHO at 450C is measured to be 3.33*10-3 M/s. Calculate the rate of production of carbon monoxide when the concentration of CH3CHO has fallen to 0.111M.
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To calculate the rate of production of carbon monoxide (CO) when the concentration of CH3CHO has fallen to 0.111 M, we can use the rate equation provided in the question.
Given:
Initial concentration of CH3CHO (C1) = 0.222 M
Final concentration of CH3CHO (C2) = 0.111 M
Rate of consumption of CH3CHO (R1) = 3.33 * 10^-3 M/s
The rate equation given states that the rate of consumption of CH3CHO varies with the concentration of CH3CHO raised to the power 1.5. This can be written as:
R1 = k * [CH3CHO]^1.5
Now, we can solve for the rate constant (k) by rearranging the equation:
k = R1 / [CH3CHO]^1.5
Substituting the given values:
k = 3.33 * 10^-3 M/s / (0.222 M)^1.5
Now that we have the rate constant, we can use it to calculate the rate of production of CO (R2) when the concentration of CH3CHO is 0.111 M:
R2 = k * [CH3CHO]^1.5
R2 = k * (0.111 M)^1.5
Substituting the value of k:
R2 = 3.33 * 10^-3 M/s / (0.222 M)^1.5 * (0.111 M)^1.5
Simplifying the equation gives the rate of production of CO when the concentration of CH3CHO has fallen to 0.111 M.
To solve this problem, we need to use the given rate expression and the stoichiometry of the reaction to calculate the rate of production of carbon monoxide (CO) when the concentration of acetaldehyde (CH3CHO) falls to 0.111 M.
Given information:
- Rate of consumption of CH3CHO (v) = 3.33 × 10^-3 M/s
- Initial concentration of CH3CHO (C1) = 0.222 M
- Final concentration of CH3CHO (C2) = 0.111 M
First, let's find the rate constant (k) by rearranging the rate equation:
v = k[C1]^1.5
Solving for k:
k = v / [C1]^1.5
= (3.33 × 10^-3 M/s) / (0.222 M)^1.5
Calculate the value of k using a calculator.
Next, we'll use the stoichiometry of the reaction to relate the rate of consumption of CH3CHO to the rate of production of CO. According to the balanced equation:
CH3CHO (g) -> CH4 (g) + CO (g)
The stoichiometric coefficient of CH3CHO is -1 (since it is being consumed) and the stoichiometric coefficient of CO is +1 (since it is being produced). Therefore, the rate of CO production (vCO) is related to the rate of CH3CHO consumption (v) by:
vCO = (1/1) × (-1/1) × v
Now we can substitute the given values and solve for the rate of production of CO:
vCO = (1/1) × (-1/1) × (3.33 × 10^-3 M/s)
= -3.33 × 10^-3 M/s
The negative sign indicates that the CO is being produced. Thus, the rate of production of carbon monoxide when the concentration of CH3CHO has fallen to 0.111 M is -3.33 × 10^-3 M/s.