Question

Question #52adc

Answer 1

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"`.