Question

The pressure of 5.0 l of gas increases from 1.50 atm to 1240 mmhg. what is the final volume of the gas, assuming constant temperature?

Answer 1

First we need to convert everything into SI units.

The initial volume of the gas is (keeping in mind that
`1 L = 0.001 m^3`:

`V_i = 5.0 L = 0.005 m^3`

The initial pressure of the gas is (keeping in mind that
`1 atm = 1.01 \cdot 10^5 Pa`:

`p_i = 1.50 atm=1.52 \cdot 10^5 Pa`

The final pressure of the gas is (keeping in mind that
`760 mmHg = 1 atm=1.01 \cdot 10^5 Pa`)

`p_f = 1240 mmHg = 1.65 \cdot 10^5 Pa`

At constant temperature, the product between pressure and volume of the gas is constant, so we can write

`p_i V_i = p_f V_f`

from which we find the final volume of the gas:

`V_f = (p_i V_i)/(p_f) = ((1.52 \cdot 10^5 Pa)(0.005 m^3))/(1.65 \cdot 10^5 Pa) =0.0046 m^3 = 4.6 L`