At 373 k, the following reaction `A(g)rarr2B(g)+C(g)` is found to be of first order. Starting with pure A, the total pressure at the end of 10 minutes was 176 mm Hg and after a long time when A was completely dissociated, it was 270 mm Hf. The pressure of A at the end of 10 minutes was

Options

A. 47 mm Hg
B. 43 mm Hg
C. 90 mm Hg
D. 86 mm Hg

Answer

A

Explanation

`{:(,A(g)rarr2B,(g)+C,(g)),("At t"=0,p,0,0),("At time"=10" min",p-x,2x,x),("At time,"t_(oo),0,2p,p):}`
At the end of `10` minutes, the total pressure was `176mmHg` . Tgus
`176=(p-x)+(2x)+(x)=p+2x`
or `2x=176-p`
At `t_(00,)` when the reaction was compele, the total pressure was `270mmHg` .
Thus, `270=2p+p=3p`
or `p=270//3=90mmHg`
Substituting this result in `Eq. `(1)` , wwe get
`2x=176-90=86mm`
or `x=43mmhg` . Pressure of `A` at the end of `10` minutes `=p-x` . Substituting the values of `p` and `x` , we get `90-43=47mmHg` .