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# Answer to Question #192837 in General Chemistry for Alexa

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.

1
2021-05-17T04:09:30-0400

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 oC 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 oC.

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).

"V \u221d T"

"V = k T"

It can also be written as

"\\frac{V_1}{T_1} = \\frac{V_2 }{T_2 }"

Convert the given temperature in oC to absolute temperature.

V 1 = 21.5 mL.

T1 = 50.0 oC = 50.0 + 273.15 = 323.15 K.

V 2 = unknown

T2 = 75.0 oC = 75.0 + 273.15 = 348.15 K

substitute all this information in the formula we have

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

Arranging this equation for V2, we have

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

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

"V_2 = 23.16 \\ mL"

which in correct significant figure is 23.2 mL.

### Hence the new volume occupied by the carbon dioxide in the pump at 75.0 oC is 23.2 mL.

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