Question

a 700 ml sample of gas has a pressure of 760.0 mm Hg at a temperature of 21.5 C.if the temperature of the gas increases to 30.0 C and the volume of the gas is compressed to 200.0 mL, what is the new pressure in kPa

Answer 1

There are two stages of this gas

1st Stage:

$V_1$ =700 ml

$P_1$ =760mm Hg

$T_1$ =21.5 degre celsius = 294.5 kelvin

Second stage:

$V_2$ =200 ml

$T_2$ =30 degre cecsius = 303 kelvin

$P_2=P_2$ (let)

From the gas eqn ,

PV=nRT

n=$\dfrac{PV}{RT}$

Now we know that in both the stages moles are conserved

$\Rightarrow$ $n_1=n_2$

$\Rightarrow$ $\dfrac{P_1V_1}{RT_1}$ = $\dfrac{P_2V_2}{RT_2}$

as R is constant from both sides, So finally

$P_2$ =$\dfrac{P_1V_1T_2}{T_1V_2}$

$P_2$ = $\dfrac{760\times700\times303}{294.5\times200}$ = 2736.77 mm Hg= 364.87 KPa