A chemistry teacher adds 50.0 mL of $1.50 M H _2 SO _4$ solution to 200 mL of water. What is the concentration of the final solution?
Use $M_i V_i=M_i V_{\text {T }}$.
A. 0.300 M
B. 0.375 M
C. 6.00 M
D. 7.50 M
Answer (2)
Identify the initial and final conditions: V 1 = 50.0 mL, M 1 = 1.50 M, V f = 250.0 mL.
Apply the dilution formula: M 1 V 1 = M f V f .
Substitute the values and solve for M f : M f = V f M 1 V 1 = 250.0 mL ( 1.50 M ) ( 50.0 mL ) .
Calculate the final concentration: M f = 0.300 M. The concentration of the final solution is 0.300 M .
Explanation
Problem Analysis and Setup We are given a problem where a chemistry teacher dilutes a solution of sulfuric acid ( H 2 S O 4 ) by adding water. We need to find the concentration of the final solution after dilution. We are given the initial volume and concentration of the sulfuric acid solution, as well as the volume of water added. We can use the formula M 1 V 1 = M f V f to solve for the final concentration.
Identify Given Values We are given:
Initial volume of H 2 S O 4 solution, V 1 = 50.0 mL
Initial concentration of H 2 S O 4 solution, M 1 = 1.50 M
Volume of water added = 200 mL
Final volume, V f = 50.0 mL + 200 mL = 250.0 mL
We want to find the final concentration, M f .
State the Formula We can use the formula for dilution:
M 1 V 1 = M f V f
Where:
M 1 is the initial concentration
V 1 is the initial volume
M f is the final concentration
V f is the final volume
Substitute Values Now, we can plug in the given values into the formula:
( 1.50 M ) ( 50.0 mL ) = M f ( 250.0 mL )
Solve for Final Concentration Next, we solve for M f :
M f = 250.0 mL ( 1.50 M ) ( 50.0 mL )
M f = 250.0 mL 75.0 M mL
M f = 0.300 M
So, the concentration of the final solution is 0.300 M.
Final Answer Therefore, the concentration of the final solution is 0.300 M.
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 create working solutions of desired concentrations. Understanding dilution calculations is crucial in many fields, including medicine, where precise concentrations of drugs are essential for patient safety.
The final concentration of the diluted sulfuric acid solution is 0.300 M. This is calculated by using the dilution formula and substituting the given values accordingly. The final concentration is derived from the initial concentration and the volumes involved in the dilution process.
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