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Sagot :
Answer:
number of moles = 0.21120811
Explanation:
To find the number of moles, given the mass of the solute, we use the formula:
[tex]\mathrm{n = \dfrac{ m }{ M } }[/tex]
[tex]\mathrm{n = number\:of\:moles\:(mol)}[/tex]
[tex]\mathrm{m = mass\:of\:solute\:(g)}[/tex]
[tex]\mathrm{M = molar\:mass\:of\:solute\:( \dfrac{ g }{ mol } )}[/tex]
Label the variables with the numbers in the problem:
[tex]\mathrm{n =\:?}[/tex]
[tex]\mathrm{m =30\:g }[/tex]
[tex]\mathrm{M =\:?\:Calculate\:the\:molar\:mass }[/tex]
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:
[tex]M({ \left Na \right }_{ 2 } { \left So \right }_{ 4 }) = m \left( Na \right) +m \left( S \right) +m \left( O \right)[/tex]
For the variables and what they mean are below for finding the molar mass of sodium sulfate:
[tex]\mathrm{M =molar\:mass }[/tex]
[tex]\mathrm{m =moles=2\:moles\:for\:Na\:,1\:mole\:for\:S,\:and\:4\:moles\:for\:O}[/tex]
[tex]\mathrm{Na =sodium=22.99\:g }[/tex]
[tex]\mathrm{S =sulfur=32.06\:g }[/tex]
[tex]\mathrm{O =oxygen=16.00\:g }[/tex]
Plug the numbers into the formula, to find the molar mass of sodium sulfate:
[tex]M({ \left Na \right }_{ 2 } { \left So \right }_{ 4 }) = m \left( Na \right) +m \left( S \right) +m \left( O \right)[/tex]
[tex]\mathrm{Substitute\:the\:values\:into\:the\:formula}[/tex]
[tex]M = 2 \left( 22.99 \right) +1 \left( 32.06 \right) +4 \left( 16.00 \right)[/tex]
[tex]\mathrm{Multiply\:2\:by\:22.99\:to\:get\:45.98\:and\:1\:by\:32.06\:to\:get\:32.06}[/tex]
[tex]\mathrm{M = 45.98+32.06+4\:(16)}[/tex]
[tex]\mathrm{Multiply\:4\:by\:16\:to\:get\:64}[/tex]
[tex]\mathrm{M = 45.98+32.06+64}[/tex]
[tex]\mathrm{Add\:45.98\:and\:32.06\:to\:get\:78.04}[/tex]
[tex]\mathrm{M = 78.04+64}[/tex]
[tex]\mathrm{Add\:78.04\:and\:64\:to\:get\:142.04}[/tex]
[tex]\mathrm{M = 142.04}[/tex]
Now that we have found the molar mass, we can calculate the number of moles in the solution of sodium sulfate with the formula:
[tex]\mathrm{n = \dfrac{ m }{ M } }[/tex]
[tex]\mathrm{n =\:?}[/tex]
[tex]\mathrm{m =30\:g }[/tex]
[tex]\mathrm{M = 142.04\:g/mol}[/tex]
[tex]\mathrm{Substitute\:the\:values\:into\:the\:formula}[/tex]
[tex]\mathrm{n = \dfrac{ 30 }{ 142.04 }}[/tex]
[tex]\mathrm{Divide\:142.04\:by\:30\:to\:get\:0.21120811}[/tex]
[tex]\mathrm{n = 0.21120811}[/tex]
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.
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