Question

A sample of n2 gas occupies 2.40 l at 20°c. if the gas is in a container that can contract or expand at constant pressure, at what temperature will the n2 occupy 4.80 l?

Answer 1

Answer: The final temperature of the gas comes out to be 313°C

Explanation:

To calculate the final temperature of the gas, we use the equation given by Charles' Law. This law states that volume of the gas is directly proportional to the temperature of the gas at constant pressure.

Mathematically,

$\frac{V_1}{T_1}=\frac{V_2}{T_2}$

where,

$V_1\text{ and }T_1$ are the initial volume and temperature of the gas.

$V_2\text{ and }T_2$ are the final volume and temperature of the gas.

We are given:

$V_1=2.40L\\T_1=20^oC=(20+273)K=293K\\V_2=4.80L\\T_2=?$

Putting values in above equation, we get:

$\frac{2.40L}{293K}=\frac{4.80L}{T_2}\\\\T_2=\frac{4.80\times 293}{2.40}=586K$

Converting the temperature from kelvins to degree Celsius, by using the conversion factor:

$T(K)=T(^oC)+273$

$586=T(^oC)+273\\T(^oC)=313^oC$

Hence, the final temperature of the system comes out to be 313°C

Answer 2

From Charle's law the volume of a fixed mass of a gas is directly proportional to the absolute temperature at constant pressure.
Therefore';
V1/T1=V2/T2
    Where; V1 = 2.40 l, T1 = 273 +20= 293 K, V2 = 4.80, and T2= ?
 2.4/293= 4.8/T2
 T2= (4.8×293)/2.4
       = 586 K or  313° C