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

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

Transcript text: 7. What volume of a 0.25 M stock solution of glucose must be used to make 500.0 mL of a $1.75 \times 10^{-2} \mathrm{M}$ 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

Solution Steps

Step 1: Understand the Dilution Formula

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).

Step 2: Substitute Known Values

Substitute the known values into the dilution formula:

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

Step 3: Solve for $V_1$

Rearrange the equation to solve for $V_1$:

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

Calculate $V_1$:

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