Question

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?

Answer 1

`"0.36 L"`

Explanation:

The idea here is that you need to figure out how many moles of carbon dioxide, `"CO"_2`, are initially dissolved in the soda by using the volume and molarity of the solution.

As you know, a molarity of `"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 `"100 kPa"` and a temperature of `0^@"C"`, are characterized by the fact that one mole of any ideal gas occupies exactly `"22.7 L"` `->` 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)|)))`