An aqueous solution is 0.12 M glucose (C6H12O6). What is the mole fraction of glucose? (Molar mass for glucose is 180 g/mol) Select one: a. 0.00215 b. 0.998 c. 0.36 d. 0.64
The Correct Answer and Explanation is:
To calculate the mole fraction of glucose in a 0.12 M aqueous solution, we need to use the following steps:
Step 1: Define molarity and molar mass
The molarity of the solution is given as 0.12 M, which means there are 0.12 moles of glucose per liter of solution. The molar mass of glucose (C6H12O6) is provided as 180 g/mol.
Step 2: Calculate the mass of glucose
To determine the number of grams of glucose in 1 liter of solution, we can use the molarity and molar mass. First, we calculate the mass of glucose in 1 liter:Mass of glucose=Moles of glucose×Molar mass of glucose\text{Mass of glucose} = \text{Moles of glucose} \times \text{Molar mass of glucose}Mass of glucose=Moles of glucose×Molar mass of glucoseMass of glucose=0.12 mol/L×180 g/mol=21.6 g\text{Mass of glucose} = 0.12 \, \text{mol/L} \times 180 \, \text{g/mol} = 21.6 \, \text{g}Mass of glucose=0.12mol/L×180g/mol=21.6g
So, in 1 liter of solution, there are 21.6 grams of glucose.
Step 3: Find the moles of water
Next, we calculate the moles of water in the solution. The mass of the solution is the sum of the mass of glucose and the mass of water. Since we are working with 1 liter of solution and the density of water is approximately 1 g/mL, the total mass of the solution is approximately 1000 g. Therefore, the mass of water is:Mass of water=1000 g−21.6 g=978.4 g\text{Mass of water} = 1000 \, \text{g} – 21.6 \, \text{g} = 978.4 \, \text{g}Mass of water=1000g−21.6g=978.4g
Now, we convert the mass of water to moles. The molar mass of water (H2O) is 18 g/mol, so:Moles of water=978.4 g18 g/mol=54.4 mol\text{Moles of water} = \frac{978.4 \, \text{g}}{18 \, \text{g/mol}} = 54.4 \, \text{mol}Moles of water=18g/mol978.4g=54.4mol
Step 4: Calculate the mole fraction of glucose
Finally, the mole fraction of glucose is the ratio of the moles of glucose to the total moles in the solution. The total moles are the sum of the moles of glucose and the moles of water:Total moles=0.12 mol+54.4 mol=54.52 mol\text{Total moles} = 0.12 \, \text{mol} + 54.4 \, \text{mol} = 54.52 \, \text{mol}Total moles=0.12mol+54.4mol=54.52mol
Now, the mole fraction of glucose is:Mole fraction of glucose=Moles of glucoseTotal moles=0.12 mol54.52 mol=0.0022\text{Mole fraction of glucose} = \frac{\text{Moles of glucose}}{\text{Total moles}} = \frac{0.12 \, \text{mol}}{54.52 \, \text{mol}} = 0.0022Mole fraction of glucose=Total molesMoles of glucose=54.52mol0.12mol=0.0022
This value rounds to approximately 0.00215.
Answer:
The mole fraction of glucose is 0.00215, so the correct choice is a. 0.00215.
