Question

Dissolve 30 g of sodium sulphate into 300 mL of water

determine the number of moles of sodium sulphate in the solution

Answer 1

number of moles = 0.21120811

Step-by-step explanation:

To find the number of moles, given the mass of the solute, we use the formula:

`\mathrm{n = ( m )/( M ) }`

`\mathrm{n = number\:of\:moles\:(mol)}`

`\mathrm{m = mass\:of\:solute\:(g)}`

`\mathrm{M = molar\:mass\:of\:solute\:( ( g )/( mol ) )}`

Label the variables with the numbers in the problem:

`\mathrm{n =\:?}`

`\mathrm{m =30\:g }`

`\mathrm{M =\:?\:Calculate\:the\:molar\:mass }`

The first thing we have to do is find the molar mass of sodium sulfate, in order for us to use the formula for finding the number of moles:

Formula for finding the molar mass of sodium sulfate:

`M({ \left Na \right }_( 2 ) { \left So \right }_( 4 )) = m \left( Na \right) +m \left( S \right) +m \left( O \right)`

For the variables and what they mean are below for finding the molar mass of sodium sulfate:

`\mathrm{M =molar\:mass }`

`\mathrm{m =moles=2\:moles\:for\:Na\:,1\:mole\:for\:S,\:and\:4\:moles\:for\:O}`

`\mathrm{Na =sodium=22.99\:g }`

`\mathrm{S =sulfur=32.06\:g }`

`\mathrm{O =oxygen=16.00\:g }`

Plug the numbers into the formula, to find the molar mass of sodium sulfate:

`M({ \left Na \right }_( 2 ) { \left So \right }_( 4 )) = m \left( Na \right) +m \left( S \right) +m \left( O \right)`

`\mathrm{Substitute\:the\:values\:into\:the\:formula}`

`M = 2 \left( 22.99 \right) +1 \left( 32.06 \right) +4 \left( 16.00 \right)`

`\mathrm{Multiply\:2\:by\:22.99\:to\:get\:45.98\:and\:1\:by\:32.06\:to\:get\:32.06}`

`\mathrm{M = 45.98+32.06+4\:(16)}`

`\mathrm{Multiply\:4\:by\:16\:to\:get\:64}`

`\mathrm{M = 45.98+32.06+64}`

`\mathrm{Add\:45.98\:and\:32.06\:to\:get\:78.04}`

`\mathrm{M = 78.04+64}`

`\mathrm{Add\:78.04\:and\:64\:to\:get\:142.04}`

`\mathrm{M = 142.04}`

Now that we have found the molar mass, we can calculate the number of moles in the solution of sodium sulfate with the formula:

`\mathrm{n = ( m )/( M ) }`

`\mathrm{n =\:?}`

`\mathrm{m =30\:g }`

`\mathrm{M = 142.04\:g/mol}`

`\mathrm{Substitute\:the\:values\:into\:the\:formula}`

`\mathrm{n = ( 30 )/( 142.04 )}`

`\mathrm{Divide\:142.04\:by\:30\:to\:get\:0.21120811}`

`\mathrm{n = 0.21120811}`

0.21120811 rounded gives you 0.2112

or if you did the problem without decimals

30 grams of sodium sulfate divided by its molecular weight – which we found to be 142 – gives us a value of 0.2113 moles.