QuestionMay 30, 2025

You want to determine the volume of 2.5M lithium nitrate solution needed to make 150 mL of a 1.0 M solution. What is M_(1) (molarity of the concentrated solution) for this dilution? 1.0 M LiNO_(3) 150 mL 2.5M LiNO_(3)

You want to determine the volume of 2.5M lithium nitrate solution needed to make 150 mL of a 1.0 M solution. What is M_(1) (molarity of the concentrated solution) for this dilution? 1.0 M LiNO_(3) 150 mL 2.5M LiNO_(3)
You want to determine the volume of 2.5M lithium nitrate solution needed to make 150 mL of a 1.0 M solution. What is M_(1) (molarity of the concentrated solution) for this dilution? 1.0 M LiNO_(3) 150 mL 2.5M LiNO_(3)

Solution
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Answer

60 mL Explanation 1. Identify the known values M_1 = 2.5 \, \text{M} (initial molarity), V_2 = 150 \, \text{mL} (final volume), M_2 = 1.0 \, \text{M} (final molarity). 2. Use the dilution formula Apply the formula **M_1 \times V_1 = M_2 \times V_2** to find V_1. 3. Solve for V_1 Rearrange to get V_1 = \frac{M_2 \times V_2}{M_1}. Substitute the values: V_1 = \frac{1.0 \, \text{M} \times 150 \, \text{mL}}{2.5 \, \text{M}}. 4. Calculate V_1 V_1 = \frac{150}{2.5} = 60 \, \text{mL}.

Explanation

1. Identify the known values<br /> $M_1 = 2.5 \, \text{M}$ (initial molarity), $V_2 = 150 \, \text{mL}$ (final volume), $M_2 = 1.0 \, \text{M}$ (final molarity).<br /><br />2. Use the dilution formula<br /> Apply the formula **$M_1 \times V_1 = M_2 \times V_2$** to find $V_1$.<br /><br />3. Solve for $V_1$<br /> Rearrange to get $V_1 = \frac{M_2 \times V_2}{M_1}$. Substitute the values: $V_1 = \frac{1.0 \, \text{M} \times 150 \, \text{mL}}{2.5 \, \text{M}}$.<br /><br />4. Calculate $V_1$<br /> $V_1 = \frac{150}{2.5} = 60 \, \text{mL}$.
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