Answer to Question #192837 in General Chemistry for Alexa

Question

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.

Answer 1

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).

$$V ∝ T$$

$$V = k T$$

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.