Question

A sample of hydrogen gas is found to occupy 906 cm of
volume at 300 K. Calculate the temperature at which it will
occupy 500 cm of volume? (Assuming amount and pressure
remains constant.)​

Answer 1

Answer:

v1=906cm3

t1=300k

v2=500cm3

t2=?

according to Charles law

v1/t1=v2/t2

906/300=500/t2

906/(300×500)=1/t2

t2=165.562k

Answer 2

The temperature at which the sample will occupy 500cm³ volume is 165.56K.

Given: Volume of sample 1 (V1)= 906cm³

The temperature of sample 1(T1) = 300K

Volume of sample 2(V2) = 500 cm³

The amount of gas and the pressure is constant

To Find: temperature of sample 2

Solution:

The Ideal Gas Law is given as

PV = nRT, where P is the pressure of the gas, V is the volume of the gas, n is the moles of the gas, R is the universal gas constant and T is the temperature of the gas.

Since the amount of gas and the pressure is constant, the number of moles and pressure will be the same for both the samples

P1 = P2 = P

n1 = n2 = n

For sample 1

P1 xV1  = n1x R xT1

P(906) = nR(300)            ..1

For sample 2

P2 x V2 = n2 x R x T2

P(500) = nR(T2)               ..2

On dividing equation 1 by equation 2, we get

906/ 500 = 300/ T2

T2 = $\frac{300(500)}{906}$

T2 = 165.56K

Therefore, the temperature at which the sample will occupy 500cm³ volume is 165.56K.