Question #52adc

1 Answer
Jul 12, 2016

Answer:

Here's what I got.

Explanation:

The number of molecules present in #"10 L"# of carbon dioxide, #"CO"_2#, actually depends on the conditions you have for pressure and temperature.

Since you didn't specify these conditions, I will assume that you're working at STP, Standard Temperature and Pressure.

STP conditions are currently defined as a pressure of #"100 kPa"# and a temperature of #0^@"C"#. Under these conditions, one mole of any ideal gas occupies #"22.7 L"# #-># this is known as the molar volume of a gas at STP.

So, if one mole occupies #"22.7 L"#, it follows that the number of moles that occupy #"10 L"# is equal to

#10 color(red)(cancel(color(black)("L CO"_2))) * overbrace("1 mole CO"_2/(22.7color(red)(cancel(color(black)("L CO"_2)))))^(color(darkgreen)("molar volume of a gas at STP")) = "0.4405 moles CO"_2#

To convert this to number of molecules, use the fact that one mole of a covalent compound contains #6.022 * 10^(23)# molecules of said compound.

#color(blue)(|bar(ul(color(white)(a/a)"1 mole" = 6.022 * 10^(23)"molecules"color(white)(a/a)|))) -># Avogadro's number

In your case, the sample of carbon dioxide will contain

#0.4405 color(red)(cancel(color(black)("moles CO"_2))) * (6.022 * 10^(23)"molec. CO"_2)/(1color(red)(cancel(color(black)("mole CO"_2)))) = 2.65 * 10^(23)"molec. CO"_2#

I'll leave the answer rounded to two sig figs< but keep in mind that you only have one sig figs for the volume of the gas

#"no. of molecules of CO"_2 = color(green)(|bar(ul(color(white)(a/a)color(black)(2.7 * 10^(23)"molecules")color(white)(a/a)|)))#

SIDE NOTE More often than not, you'll find STP conditions defined as a pressure of #"1 atm"# and a temperature of #0^@"C"#.

This is the old definition of STP for which one mole of any ideal gas occupies #"22.4 L"#. If this is the value of the molar volume of a gas at STP given to you, simply redo the calculations using #"22.4 L"# instead of #"22.7 L"#.