Question

The reaction, $A\left(g\right)+2B\left(g\right)\to C\left(g\right)+D\left(g\right)$, is an elementary process. In an experiment involving this reaction, the initial partial pressures of A and B are $P_A=0.60$ atm and $P_B=0.80$ atm respectively. When $P_C=0.20$ atm, the rate of the reaction relative to the initial rate is:

• A. 1/6
• B. 1/12
• C. 1/36
• D. 1/18

Answer 1

The correct option is A 1/6

The expression for the initial rate is $r_o=K\left[A\right][B{]}^2=K(0.60\left)\right(0.80{)}^2$...... (1)
After some time, the pressure of C is 0.20 atm.
Hence, the pressures of A and B are $0.60-0.20=0.40atmand0.80-2\left(0.20\right)=0.40atm$ respectively.
The expression for the rate becomes $r=k\left[A\right][B{]}^2=K(0.40\left)\right(0.40{)}^2$...... (2)
Divide equation (2) with equation (1)
$\frac{r_o}{r_1}=\frac{k\left[A\right][B{]}^2=K(0.60\left)\right(0.80{)}^2}{k\left[A\right][B{]}^2=K(0.40\left)\right(0.40{)}^2}=\frac{1}{6}$.