# How do you calculate the number of moles from volume?

It depends on the substance whose volume you know.

If you have a pure liquid or a solid, you use its to calculate its mass and then divide the mass by the molar mass.

If you have a solution, you multiply the by the volume in litres.

MOLES FROM VOLUME OF PURE LIQUID OR SOLID

There are two steps:

1. Multiply the volume by the density to get the mass.
2. Divide the mass by the molar mass to get the number of moles.

Example

How many moles are in 10.00 mL of acetic anhydride? The molar mass of acetic anhydride is 102.1 g/mol and its density is 1.080 g/mL?

Solution

The formula for density is

##color(blue)(|bar(ul(color(white)(a/a) ρ = m/V color(white)(a/a)|)))” “##

where ##ρ## is the density, ##m## is the mass, and ##V## is the volume of the sample.

We can rearrange the formula to get

##m = V × ρ##

##”mass” = 10.00 color(red)(cancel(color(black)(“mL”))) × “1.080 g”/(1 color(red)(cancel(color(black)(“mL”)))) = “10.80 g”##

##n = 10.80 color(red)(cancel(color(black)(“g”))) × “1 mol”/(102.1color(red)(cancel(color(black)(“g”)))) = “0.1058 mol”##

MOLES FROM VOLUME OF SOLUTION

Molarity is the number of moles of a substance in one litre of solution.

##color(blue)(|bar(ul(color(white)(a/a) M = n/Vcolor(white)(a/a)|)))” “##

where ##n## is the number of moles and ##V## is the volume in litres.

We can rearrange this equation to get the number of moles:

##n = M × V##

Example

How many moles of ##”NaCl”## are contained in 0.300 L of 0.400 mol/L ##”NaCl”## solution?

Solution

##n = 0.300 color(red)(cancel(color(black)(“L soln”))) × “0.400 mol NaCl”/(1 color(red)(cancel(color(black)(“L soln”)))) = “0.120 mol NaCl”##

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