Question

How many moles of K2SO4 are in 45 g of K2SO4?

O 0.82 moles
O 7.8 x 103 moles
O 1.333 moles
0.26 moles
0.019 moles

Answer 1

• Answer:

`\Large{\boxed{\sf 0.26 \: moles}}`

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• Explanation:

The relationship between the mass, the number of moles, and the molar mass is the following:

`\Large{\sf n = (m)/(M) }`

Where:

• n is the number of moles in mol.
• m is the mass in g.
• M is the molar mass in g/mol.

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[ Definition: ]

The molar mass of a compound corresponds to the mass of one mole of that substance.

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We have to determine the molar mass of a molecule of
`\sf K_2SO_4`, also known as potassium sulfate.

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Using a periodic table of elements, we get:

M(K) = 39.1 g/mol

M(S) = 32 g/mol

M(O) = 16 g/mol

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We are now able to calculate the molar mass of one molecule of potassium sulfate.

`\sf M(K_2SO_4) = 2M(K) + M(S) + 4M(O) \\ \sf = 2(39.1) + 32 + 4(16) \\ \sf = 78.2 + 32 + 64 \\ \\ = \boxed{\sf 174.2 \: g/mol}`

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Now, let's substitute our values into the formula:

`\sf n = \frac{\overbrace{45 \: g}^(m)}{ \underbrace{174.2 \: g/mol}_(M(K_2SO_4))} \approx 0.25832 \: moles`

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Rounding our answer to the nearest hundredth, we get:

`\boxed{\boxed{\sf n = 0.26 \: moles}}`