A Student Takes A Measured Volume Of 3.00 M HCl To Prepare A 50.0 ML Sample Of 1.80 M HCl. What Volume Of 3.00 M HCl Did The Student Use To Make The Sample?Use The Formula: $M_1 V_1 = M_2 V_2$A. 3.70 ML B. 16.7 ML C. 30.0 ML D. 83.3 ML

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Introduction

In chemistry, dilution is a crucial concept that involves reducing the concentration of a solution by adding a solvent. This process is essential in various laboratory settings, including titrations, where the concentration of a substance needs to be accurately determined. In this article, we will explore a scenario where a student is tasked with preparing a 50.0 mL sample of 1.80 M HCl by diluting a 3.00 M HCl solution. We will use the formula M1V1=M2V2M_1 V_1 = M_2 V_2 to calculate the volume of 3.00 M HCl used by the student.

The Dilution Formula

The dilution formula is a fundamental concept in chemistry that allows us to calculate the volume of a solution before and after dilution. The formula is given by:

M1V1=M2V2M_1 V_1 = M_2 V_2

where:

  • M1M_1 is the initial concentration of the solution (in moles per liter, M)
  • V1V_1 is the initial volume of the solution (in liters, L)
  • M2M_2 is the final concentration of the solution (in moles per liter, M)
  • V2V_2 is the final volume of the solution (in liters, L)

Calculating the Volume of 3.00 M HCl

In this scenario, the student wants to prepare a 50.0 mL sample of 1.80 M HCl by diluting a 3.00 M HCl solution. We can use the dilution formula to calculate the volume of 3.00 M HCl used by the student.

First, we need to convert the initial and final volumes from milliliters (mL) to liters (L). We know that 1 L = 1000 mL, so:

V1=3.00 M×1 L=3.00 LV_1 = 3.00 \text{ M} \times 1 \text{ L} = 3.00 \text{ L}

V2=50.0 mL×1 L1000 mL=0.0500 LV_2 = 50.0 \text{ mL} \times \frac{1 \text{ L}}{1000 \text{ mL}} = 0.0500 \text{ L}

Now, we can plug in the values into the dilution formula:

3.00 M×V1=1.80 M×0.0500 L3.00 \text{ M} \times V_1 = 1.80 \text{ M} \times 0.0500 \text{ L}

To solve for V1V_1, we can divide both sides of the equation by 3.00 M:

V1=1.80 M×0.0500 L3.00 MV_1 = \frac{1.80 \text{ M} \times 0.0500 \text{ L}}{3.00 \text{ M}}

V1=0.0900 L3.00 MV_1 = \frac{0.0900 \text{ L}}{3.00 \text{ M}}

V1=0.0300 LV_1 = 0.0300 \text{ L}

Since we want to find the volume in milliliters, we can multiply the result by 1000:

V1=0.0300 L×1000 mL1 LV_1 = 0.0300 \text{ L} \times \frac{1000 \text{ mL}}{1 \text{ L}}

V1=30.0 mLV_1 = 30.0 \text{ mL}

Conclusion

In this article, we used the dilution formula to calculate the volume of 3.00 M HCl used by a student to prepare a 50.0 mL sample of 1.80 M HCl. We found that the student used 30.0 mL of 3.00 M HCl to make the sample.

Answer

The correct answer is:

  • C. 30.0 mL

Discussion

This problem requires the student to apply the dilution formula to calculate the volume of a solution before and after dilution. The student needs to convert the initial and final volumes from milliliters to liters, plug in the values into the dilution formula, and solve for the unknown volume. This problem is an excellent example of how the dilution formula can be used to calculate the volume of a solution in various laboratory settings.

Key Takeaways

  • The dilution formula is a fundamental concept in chemistry that allows us to calculate the volume of a solution before and after dilution.
  • The dilution formula is given by M1V1=M2V2M_1 V_1 = M_2 V_2, where M1M_1 is the initial concentration, V1V_1 is the initial volume, M2M_2 is the final concentration, and V2V_2 is the final volume.
  • To calculate the volume of a solution before and after dilution, we need to convert the initial and final volumes from milliliters to liters.
  • The dilution formula can be used to calculate the volume of a solution in various laboratory settings, including titrations.
    A Student's Dilution Dilemma: Calculating the Volume of 3.00 M HCl ===========================================================

Q&A: Dilution Dilemmas

Q: What is the dilution formula?

A: The dilution formula is a fundamental concept in chemistry that allows us to calculate the volume of a solution before and after dilution. The formula is given by:

M1V1=M2V2M_1 V_1 = M_2 V_2

where:

  • M1M_1 is the initial concentration of the solution (in moles per liter, M)
  • V1V_1 is the initial volume of the solution (in liters, L)
  • M2M_2 is the final concentration of the solution (in moles per liter, M)
  • V2V_2 is the final volume of the solution (in liters, L)

Q: How do I use the dilution formula to calculate the volume of a solution?

A: To use the dilution formula, you need to follow these steps:

  1. Convert the initial and final volumes from milliliters to liters.
  2. Plug in the values into the dilution formula.
  3. Solve for the unknown volume.

Q: What if I don't know the initial volume of the solution?

A: If you don't know the initial volume of the solution, you can use the dilution formula to calculate it. Simply rearrange the formula to solve for V1V_1:

V1=M2V2M1V_1 = \frac{M_2 V_2}{M_1}

Q: Can I use the dilution formula to calculate the concentration of a solution?

A: Yes, you can use the dilution formula to calculate the concentration of a solution. Simply rearrange the formula to solve for M2M_2:

M2=M1V1V2M_2 = \frac{M_1 V_1}{V_2}

Q: What if I have a solution with a concentration of 0.50 M and I want to dilute it to 0.10 M? How much solvent do I need to add?

A: To calculate the amount of solvent needed to dilute the solution, you can use the dilution formula. Let's say you have 100 mL of 0.50 M solution and you want to dilute it to 0.10 M. First, convert the volumes from milliliters to liters:

V1=100 mL×1 L1000 mL=0.100 LV_1 = 100 \text{ mL} \times \frac{1 \text{ L}}{1000 \text{ mL}} = 0.100 \text{ L}

V2=?V_2 = ?

Since you want to dilute the solution to 0.10 M, you can set up the equation:

0.50 M×0.100 L=0.10 M×V20.50 \text{ M} \times 0.100 \text{ L} = 0.10 \text{ M} \times V_2

To solve for V2V_2, divide both sides of the equation by 0.10 M:

V2=0.50 M×0.100 L0.10 MV_2 = \frac{0.50 \text{ M} \times 0.100 \text{ L}}{0.10 \text{ M}}

V2=0.500 LV_2 = 0.500 \text{ L}

Since you want to dilute the solution to 0.10 M, you need to add 0.400 L of solvent (0.500 L - 0.100 L).

Q: What are some common mistakes to avoid when using the dilution formula?

A: Some common mistakes to avoid when using the dilution formula include:

  • Not converting the volumes from milliliters to liters.
  • Not plugging in the correct values into the formula.
  • Not solving for the correct variable.
  • Not checking the units of the answer.

Conclusion

In this article, we have discussed the dilution formula and how to use it to calculate the volume of a solution before and after dilution. We have also answered some common questions about the dilution formula and provided examples of how to use it in different scenarios. By following the steps outlined in this article, you should be able to use the dilution formula with confidence and accuracy.