Question

A popular brand of cola contains 7.80 g of carbon dioxide dissolved in 1.00 L of soft drink. If the evaporating carbon dioxide is trapped in a cylinder at 1.00 atm and 18.0°C, what volume does the gas occupy?

Answer 1

Hello and thank you for your question.

Let's assume the carbon dioxide an ideal gas, and that the whole 7.80 g have evaporated into the cylinder.

Let's recall the ideal gas formula:

$PV=nRT$

We clear volume:

$V=\frac{nRT}{P}$

n is the number of mol of the substance we have.

We can determine it as:

$n=\frac{mass}{molar mass}$

We can find the molar mass of the carbon dioxide on charts.

$n=\frac{7.8g}{44.01g/mol}\approx 0.177mol$

Now for the constant R is already given as:

$R=0.082L.atm/mol.K$

We just have to make one small change to apply the formula, convert Celsius into Kelvin:

$18^{\circ}C+273.15=291.15K$

We proceed to apply the formula:

$V=\frac{(0.177mol)(0.082L.atm/mol.K)(291.15K)}{1.00 atm}\approx 4.23L$

Good luck!