Problem 6 - Chemistry A Guided Inquiry

Question

Verify that when \(10.0 \mathrm{~g}\) of sodium sulfate dissolves in water: a) there are \(7.04 \times 10^{-2}\) moles of sodium sulfate in the water. b) there are \(7.04 \times 10^{-2}\) moles of sulfate in the water. c) there are \(14.1 \times 10^{-2}\) moles of sodium in the water.

Step-by-Step Solution

Answer

a) Verified. There are indeed \(7.04 \times 10^{-2}\) moles of sodium sulfate in 10.0g of the substance.\n b) Verified. There are indeed \(7.04 \times 10^{-2}\) moles of sulfate ions in 10.0g of sodium sulfate. \n c) Verified. There are indeed \(14.1 \times 10^{-2}\) moles of sodium ions in 10.0g of sodium sulfate.

Step 1: Calculate the molar mass of sodium sulfate

The molar mass of a compound is calculated by adding together the atomic masses of each atom in the compound. For sodium sulfate (Na2SO4), the atomic mass of sodium (Na) is 23.0g/mol, sulfur (S) is 32.1g/mol and oxygen (O) is 16.0g/mol. By adding the atomic masses, we find the molar mass of sodium sulfate to be \( (2 \times 23.0) + 32.1 + (4 \times 16.0) = 142.1 \mathrm{~g/mol} \).

Step 2: Calculate the moles of sodium sulfate

The number of moles of a substance can be calculated using the formula: \[ \text{number of moles} = \frac{\text{mass of the substance}}{\text{molar mass of the substance}} \] Using this formula, the number of moles of sodium sulfate in 10.0g would be \( \frac{10.0\mathrm{~g}}{142.1\mathrm{~g/mol}} = 7.04 \times 10^{-2}\) moles.

Step 3: Verify the moles of sulfate

Each molecule of sodium sulfate consists of one sulfate ion. So, the number of moles of sulfate ions will be equal to the number of moles of sodium sulfate. Which is, \(7.04 \times 10^{-2}\) moles.

Step 4: Calculate the moles of sodium ions

Each molecule of sodium sulfate consists of two sodium ions. So, the number of moles of sodium ions will be twice the number of moles of sodium sulfate. So, the number of moles of sodium ions would be \(2 \times 7.04 \times 10^{-2}\) which equals \(14.1 \times 10^{-2}\) moles.