# Question 5bc68

Aug 27, 2016

$\text{0.45 L}$

#### Explanation:

The idea here is that you need to use the molarity and volume of the solution to determine how many moles of carbon dioxide you have dissolved in the solution.

Once you know that, use the molar volume of a gas at STP to calculate the volume that many moles would occupy under STP conditions.

So, molarity is defined as the number of moles of solute, which in your case is carbon dioxide, ${\text{CO}}_{2}$, present in one liter of solution.

In this regard, a $\text{0.1-M}$ solution will contain $0.1$ moles of carbon dioxide for every liter of solution. This means that your sample will contain

200 color(red)(cancel(color(black)("mL"))) * (1color(red)(cancel(color(black)("L"))))/(10^3color(red)(cancel(color(black)("mL")))) * "0.1 moles CO"_2/(1color(red)(cancel(color(black)("L")))) = "0.02 moles CO"_2

Now, STP conditions are currently defined as a pressure of $\text{100 kPa}$ and a temperature of ${0}^{\circ} \text{C}$. Under these specific conditions, one mole of any ideal gas occupies $\text{22.7 L}$.

This is known as the molar volume of a gas at STP. Use this value to determine the volume occupied under STP conditions by your sample

0.02color(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)("0.45 L")color(white)(a/a)|)))#

I'll leave the answer rounded to two sig figs, but keep in mind that you only have one sig fig for your values.

SIDE NOTE More often than not, the molar volume of a gas at STP will correspond to the old definition of STP conditions, which was a pressure of $\text{1 atm}$ and a temperature of ${0}^{\circ} \text{C}$.

Under these conditions for pressure and temperature, one mole of any ideal gas occupies $\text{22.4 L}$. If these are the values given to you, simply redo the last calculation by using $\text{22.4 L}$ instead of $\text{22.7 L}$.