Question

For the first order gaseous reaction, $x\left(g\right)\to 2y\left(g\right)+z\left(g\right)$, the initial pressure, $P_x=90$ mm Hg. The pressure after 10 minutes is 180 mm Hg. The rate constant of the reaction is:

• A. $2\times {10}^{-3}se{c}^{-1}$
• B. $2\times {10}^{3}se{c}^{-1}$
• C. $1.15\times {10}^{-3}se{c}^{-1}$
• D. $1.15\times {10}^{3}se{c}^{-1}$

Answer 1

The correct option is C $1.15\times {10}^{-3}se{c}^{-1}$

The inital pressure of x, $P_x$is 90 mm Hg.

Total pressure after 10 minute is 180 mm Hg. Let X be the change in pressure of x.

Total pressure will be $(P_x-X)+2X+X=P_x+2X=90+2X=180$ or $X=45mm.$

The expression for the rate constant is $k=\frac{2.303}{t}log\frac{a}{a-X}=\frac{2.303}{10\times 60}log\frac{90}{90-45}=1.15\times {10}^{-3}se{c}^{-1}.$