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Some fertilizer blends contain magnesium nitrate $\left( Mg _{\left( NO _3\right)_2}\right)$. Suppose that a chemist has 1.24 liters of a 2.13 M solution of magnesium nitrate. If the chemist dilutes the solution to 1.60 M, what is the volume of the new solution?
Express your answer to three significant figures.
The volume of the new solution is $\square$ liters.
Answer (2)
Use the dilution formula: M 1 V 1 = M 2 V 2 .
Substitute the given values: M 1 = 2.13 M , V 1 = 1.24 liters , M 2 = 1.60 M .
Solve for V 2 : V 2 = M 2 M 1 V 1 = 1.60 ( 2.13 ) ( 1.24 ) = 1.65075 liters .
Round to three significant figures: V 2 = 1.65 liters .
Explanation
Problem Analysis We are given the initial volume and concentration of a magnesium nitrate solution, and the final concentration after dilution. We need to find the final volume of the diluted solution.
Dilution Formula We will use the dilution formula, which states that the product of the initial molarity and volume is equal to the product of the final molarity and volume: M 1 V 1 = M 2 V 2 where: M 1 = initial concentration V 1 = initial volume M 2 = final concentration V 2 = final volume
Given Values We are given: M 1 = 2.13 M V 1 = 1.24 liters M 2 = 1.60 M We need to find V 2 .
Solving for Final Volume Rearrange the formula to solve for V 2 :
V 2 = M 2 M 1 V 1
Calculation Plug in the given values: V 2 = 1.60 M ( 2.13 M ) ( 1.24 liters ) V 2 = 1.60 2.6412 liters V 2 = 1.65075 liters
Rounding We need to express the answer to three significant figures. Therefore, we round 1.65075 to 1.65.
Final Answer The volume of the new solution is 1.65 liters.
Examples
Dilution is a common practice in chemistry, biology, and even everyday life. For example, when you add water to concentrated juice, you are diluting it. Similarly, in a lab, scientists often dilute stock solutions to achieve the desired concentration for experiments. Understanding dilution calculations ensures accurate preparation of solutions, which is crucial in many scientific and practical applications. The formula M 1 V 1 = M 2 V 2 helps to determine the required volumes or concentrations for these dilutions, ensuring precision and accuracy in various fields.
To find the new volume after dilution, we used the formula M 1 V 1 = M 2 V 2 . By substituting the given values and calculating, we found the volume to be approximately 1.65 liters. This indicates how dilution impacts solution concentration and volume.
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