The concentration of CO_2 in a can of soda is approximately 0.045 M. If all of the CO_2 in a 12 ounce soda evolves from solution, how many liters would the CO_2 gas take up at STP?

Aug 7, 2016

$\text{0.36 L}$

Explanation:

The idea here is that you need to figure out how many moles of carbon dioxide, ${\text{CO}}_{2}$, are initially dissolved in the soda by using the volume and molarity of the solution.

As you know, a molarity of $\text{0.045 M}$ means that every liter of solution, which in your case is soda, will contain $0.045$ moles of carbon dioxide.

This means that your

12 color(red)(cancel(color(black)("oz"))) * (29.57 color(red)(cancel(color(black)("mL"))))/(1color(red)(cancel(color(black)("oz")))) * "1 L"/(10^3color(red)(cancel(color(black)("mL")))) = "0.35484 L"

sample of soda will contain

0.35484 color(red)(cancel(color(black)("L soda"))) * "0.045 moles CO"_2/(1color(red)(cancel(color(black)("L soda")))) = "0.01597 moles CO"_2

Now, you are told that all of the moles of carbon dioxide evolve from the solution.

As you know, STP conditions, which are defined as a pressure of $\text{100 kPa}$ and a temperature of ${0}^{\circ} \text{C}$, are characterized by the fact that one mole of any ideal gas occupies exactly $\text{22.7 L}$ $\to$ this is known as the molar volume of a gas at STP.

This means that your sample of carbon dioxide will occupy

0.01597 color(red)(cancel(color(black)("moles CO"_2))) * "22.7 L"/(1color(red)(cancel(color(black)("mole CO"_2)))) = color(green)(|bar(ul(color(white)(a/a)color(black)("0.36 L")color(white)(a/a)|)))