Question #192837

A gas sample has a volume of 21.5 mL and it is at 50.0 °C. When the amount of gas and pressure remain constant, find the new volume of Carbon dioxide in the pump if the temperature is increased to 75.0 °C.

Expert's answer

**Q192837**

A gas sample has a volume of 21.5 mL and it is at 50.0 °C. When the amount of gas and pressure remain constant, find the new volume of Carbon dioxide in the pump if the temperature is increased to 75.0 °C.

**Solution: **

The amount of gas and pressure is constant.

The volume occupied by the sample of gas at 50.0 ^{o}C is 21.5 mL.

We are asked to find the new volume of carbon dioxide in the pump when the temperature is increased to 75.0 ^{o}C.

We can use Charle's law here.

**Charle's law: ** For a fixed quantity of gas and at constant pressure, the volume occupied by the gas is directly proportional to the absolute temperature(K).

It can also be written as

Convert the given temperature in ^{o}C to absolute temperature.

V_{ 1} = 21.5 mL.

T_{1} = 50.0 ^{ o}C = 50.0 + 273.15 = 323.15 K.

V _{2} = unknown

T_{2} = 75.0^{ o}C = 75.0 + 273.15 = 348.15 K

substitute all this information in the formula we have

Arranging this equation for V_{2}, we have

"\\frac{V_2 }{348.15 \\ K } = \\frac{21.5 \\ mL }{323.15 \\ K }"

which in correct significant figure is 23.2 mL.

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