Problem 11 - Chemistry A Guided Inquiry

Question

Verify that when \(5.26 \mathrm{~g}\) of glucose, \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\), dissolves in water: a) there are \(2.92 \times 10^{-2}\) moles of glucose in the water. b) there are \(1.76 \times 10^{22}\) molecules of glucose in the water.

Step-by-Step Solution

Answer

The given quantities of glucose are correct. There are indeed \(2.92 \times 10^{-2}\) moles and \(1.76 \times 10^{22}\) molecules of glucose dissolved in the water.

Step 1: Calculating moles of glucose

Using the molar mass of glucose, you can calculate the moles of glucose. The moles are calculated by dividing the given mass by the molar mass: \(\text{Moles} = \frac{\text{Mass}}{\text{Molar mass}} = \frac{5.26g}{180.156g/mol} = 2.92 \times 10^{-2}\) moles.

Step 2: Verifying the number of moles

Compare the calculated moles with the given value in the problem: \(2.92 \times 10^{-2}\) moles. Therefore, the given molar quantity is correct.

Step 3: Calculating the number of molecules

Now, using Avogadro's number, calculate the number of molecules. The number of molecules is given by the product of the number of moles and Avogadro's number: Number of molecules = \(\text{Moles} \times \text{Avogadro's number} = 2.92 \times 10^{-2} \times 6.02214076 × 10^{23} = 1.76 \times 10^{22}\) molecules.

Step 4: Verifying the number of molecules

Compare this calculated number of molecules with the given value in the problem: \(1.76 \times 10^{22}\) molecules. This confirms the given number of molecules is correct.