Questions: What volume of a 0.25 M stock solution of glucose must be used to make 500.0 mL of a 1.75 × 10^-2 M glucose solution in water? (a) 0.035 liter (b) 2.19 liter (c) 0.088 liter (d) 0.500 liter (e) 0.175 liter

Solution Steps

To find the volume of the stock solution needed, we use the dilution formula:

\[ C_1V_1 = C_2V_2 \]

where:

• \(C_1\) is the concentration of the stock solution (0.25 M),
• \(V_1\) is the volume of the stock solution needed,
• \(C_2\) is the concentration of the diluted solution (\(1.75 \times 10^{-2} \, \text{M}\)),
• \(V_2\) is the volume of the diluted solution (500.0 mL or 0.500 L).

Substitute the known values into the dilution formula:

\[ 0.25 \times V_1 = 1.75 \times 10^{-2} \times 0.500 \]

Rearrange the equation to solve for \(V_1\):

\[ V_1 = \frac{1.75 \times 10^{-2} \times 0.500}{0.25} \]

Calculate \(V_1\):

\[ V_1 = \frac{0.00875}{0.25} = 0.035 \]

Final Answer