Question

A gas occupies a volume of 1000 CC at 0°C and 760 mm pressure find the volume of gas if temperature of the gas is increased by one fifth and its pressure is increased one and half times. (Ans-800 cc)​

Answer 1

Given :

A gas occupies a volume of 1000 CC at 0°C and 760 mm pressure. Temperature of the gas is increased by one fifth and its pressure is increased one and half times.

To Find :

The Volume.

Solution :

Analysis :

Here we have to use gas equation which is derived from Boyle's Law and Charle's Law. We have our initial conditions. So from that we can make out the final conditions and find the final volume.

Required Formula :

$\boxed{\bf\dfrac{P_1V_1}{T_1}=\dfrac{P_2V_2}{T_2}}$

where,

• P₁ = Initial Pressure
• V₁ = Initial Volume
• T₁ = Initial Temperature

• P₂ = Final Pressure
• V₂ = Final Volume
• T₂ = Final Temperature

Explanation :

Initial Conditions :

• P₁ = 760 mm Hg
• V₁ = 1000 cc
• T₁ = 0°C = 273 K

Final Conditions :

It is said that the temperature of the gas is increased by one fifth.

So,

T₂ = 273 + 1/5 × 273

= 273 + 273/5

= (1365 + 273)/5

= 1638/5

= 327.6 K

Now, it is that pressure is increased one and half times.

So,

P₂ = $\sf1\dfrac{1}{2}\times760$

= 3/2 × 760

= 3 × 380

= 1140 mm Hg

• P₂ = 1140 mm Hg
• V₂ = V cc
• T₂ = 327.6 K

Using gas equation,

$\\ :\implies\sf\dfrac{P_1V_1}{T_1}=\dfrac{P_2V_2}{T_2}$

Substituting the required values from the above information,

$\\ :\implies\sf\dfrac{760\times1000}{273}=\dfrac{1140\times V}{327.6}$

Removing the point from 327.6,

$\\ :\implies\sf\dfrac{760\times1000}{273}=\dfrac{1140\times V\times10}{3276}$

$\\ :\implies\sf\dfrac{760\times1000\times3276}{273\times1140\times10}=V$

$\\ :\implies\sf\dfrac{76\not{0}\times100\not{0}\times3276}{273\times114\not{0}\times1\not{0}}=V$

$\\ :\implies\sf\dfrac{76\times100\times3276}{273\times114\times1}=V$

$\\ :\implies\sf\dfrac{76\times\cancel{100}\ \ ^{50}\times3276}{273\times\cancel{114}\ \ ^{57}}=V$

$\\ :\implies\sf\dfrac{76\times50\times3276}{273\times57}=V$

$\\ :\implies\sf\dfrac{76\times50\times\cancel{3276}\ \ ^{1092}}{\cancel{273}\ \ ^{91}\times57}=V$

$\\ :\implies\sf\dfrac{76\times50\times1092}{91\times57}=V$

$\\ :\implies\sf\dfrac{4149600}{5187}=V$

$\\ :\implies\sf\cancel{\dfrac{4149600}{5187}}=V$

$\\ :\implies\sf800=V$

$\\ \therefore\boxed{\bf V=800\ cc.}$

The volume of the gas is 800 cc.

Explore More :

The gas equation is an equation used in chemical calculations for calculating the change in volumes of gases when pressure and temperature both undergo a change thereby giving a simultaneous effect of changes of temperature and pressure on the volume of a given mass of a dry gas.