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?

Md Ariful Islam

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Md Ariful Islam

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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 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 .

This means that your sample of carbon dioxide will occupy

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

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