Question

If 10.5 L of a gas at 0.98 atm has its pressure increased to 1.50 atm, what is the new volume?

Answer 1

The new volume of this gas is 6.86 liters.

Assumption: the temperature of this gas stays the same, and this gas is ideal such that Boyle's Law applies.

Step-by-step explanation:

By Boyle's Law, the volume of an ideal gas shall be inversely proportional to the pressure on it when temperature stays the same (as in an isothermal process.)

In other words,

`\displaystyle V \propto (1)/(P)`,

where

• 
  `V` is the volume of the gas, and
• 
  `P` is the pressure on the gas.

`P_1 \cdot V_1 = P_2 \cdot V_2`.

`\displaystyle V_2 = (P_1 \cdot V_1 )/(P_2)`.

Assume that this gas is ideal. Also assume that this increase in pressure is isothermal. Apply Boyle's Law to find the new volume of this gas:

`\displaystyle V_2 = (P_1 \cdot V_1 )/(P_2) = \rm (0.98\;atm * 10.5\; L)/(1.50\; atm) = 6.86\; L`.