How many molecules of #CO_2# gas at 713 mmHg and 56.7°C are present in 10.5 L?
1 Answer
Explanation:
Your strategy here will be to
- use the ideal gas law equation to determine how many moles of gas you have under those conditions for pressure and temperature
- use Avogadro's number to determine how many molecules of carbon dioxide would be found in that many moles
So, the ideal gas law equation looks like this
#color(blue)(PV = nRT)" "# , where
The important thing to be aware of here is that the units you have for pressure, temperature, and volume must match those used in the expression of the universal gas constant.
You will thus need to convert the pressure of the gas from mmHg to atm and its temperature from degrees Celsius to Kelvin.
So, rearrange the ideal gas law equation to solve for
#PV = nRT implies n = (PV)/(RT)#
#n = (713/760 color(red)(cancel(color(black)("atm"))) * 10.5color(red)(cancel(color(black)("L"))))/(0.0821(color(red)(cancel(color(black)("atm"))) * color(red)(cancel(color(black)("L"))))/("mol" * color(red)(cancel(color(black)("K")))) * (273.15 + 56.7)color(red)(cancel(color(black)("K"))))#
#n = "0.36375 moles CO"_2#
Now, one mole of any substance contains exactly
This means that your sample of carbon dioxide will contain
#0.36375 color(red)(cancel(color(black)("moles CO"_2))) * (6.022 * 10^(23)"molec. CO"_2)/(1color(red)(cancel(color(black)("mole CO"_2)))) = color(green)(2.19 * 10^(23)"molec. CO"_2#
The answer is rounded to three sig figs.