Answer to Question #245026 in Physics for emily

Question

A 1.5L bottle of generic soft-drink contains 14g of carbon dioxide dissolved in its volume. After opening of the bottle, the evaporating carbon dioxide is trapped in a cylinder at 1.1atm and 17°C, what volume does the gas occupy?

Give your answer in litres to the nearest tenth of a litre.

1atm=101300Pa

Take the universal gas constant to be R=8.31J/(mole kg), the molar mass of CO₂ to be 44g/mol, and absolute zero to be at -273°C.

Answer 1

According to ideal gas law:

$$P_0V_0=\frac m{\Mu}RT.$$

Find the initial volume of carbon dioxide at 1 atm (normal pressure):

$$V_0=\frac{mRT}{P_0\Mu}.$$

Apply the combined gas law:

$$\frac{P_0V_0}{T}=\frac{P_1V_1}{T},\\\space\\ V_1=V_0\frac{P_0}{P_1}=\frac{mRT}{P_1\Mu},\\\space\\ V_1=\frac{0.014·8.314·(273+17)}{(1.1·101300)(44·10^{-3})}=6.89·10^{-3}\text{ m}^3,$$

or around 7 L.