Question

A 5.00–liter sample of nitrogen gas at 27°C and 320 mm Hg is heated until it occupies a volume of 15.0 liters. If the pressure remains unchanged, the final temperature of the gas is?

Answer 1

The final temperature of the gas will be 900. K.

SInce pressure and number of moles are kept constant, you can use Charles' Law to figure out what the final temperature of the gas will be.

According to Charles' Law, volume and temperature have direct relationship when pressure and number of moles are kept constant.

This means that the hotter the gas, the bigger the volume it occupies. Because the final volume is bigger than the initial volume. you can easily predict that the final temperature ill be higher than the inital `27^@"C"`.

`V_1/T_1 = V_2/T_2`, where

`V_1`, `T_1` - the volume and temperature at an initial state;
`V_2`, `T_2` - the volume and temperature at final state.

In your case, you get

`T_2 = V_2/V_1 * T_1`

`T_2 = (15.0cancel("L"))/(5.00cancel("L")) * (273.15 + 27)"K" = "900.45 K"`

The volume is three times bigger, so the temperature must be three times higher, given that pressure and number of moles are constant.