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: $M_i V_i = M_f V_f$.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 process that involves reducing the concentration of a solution by adding a solvent. This process is essential in various applications, including laboratory experiments, industrial processes, and even everyday life. In this article, we will explore a scenario where a student needs to prepare a 50.0 mL sample of 1.80 M HCl by diluting a 3.00 M HCl solution. We will use the formula MiVi=MfVfM_i V_i = M_f V_f 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 helps us calculate the volume of a solution before and after dilution. The formula is given by:

MiVi=MfVfM_i V_i = M_f V_f

where:

  • MiM_i is the initial concentration of the solution (in moles per liter, M)
  • ViV_i is the initial volume of the solution (in liters, L)
  • MfM_f is the final concentration of the solution (in moles per liter, M)
  • VfV_f is the final volume of the solution (in liters, L)

Calculating the Volume of HCl

In this scenario, the student needs 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 mL = 0.001 L, so:

Vi=3.00 M×0.001 L=0.003 LV_i = 3.00 \text{ M} \times 0.001 \text{ L} = 0.003 \text{ L}

Vf=50.0 mL×0.001 L=0.05 LV_f = 50.0 \text{ mL} \times 0.001 \text{ L} = 0.05 \text{ L}

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

MiVi=MfVfM_i V_i = M_f V_f

3.00 M×0.003 L=1.80 M×0.05 L3.00 \text{ M} \times 0.003 \text{ L} = 1.80 \text{ M} \times 0.05 \text{ L}

Simplifying the equation, we get:

0.009 L=0.09 L0.009 \text{ L} = 0.09 \text{ L}

However, this is not correct. We made a mistake in our calculation. Let's re-evaluate the equation:

MiVi=MfVfM_i V_i = M_f V_f

3.00 M×Vi=1.80 M×0.05 L3.00 \text{ M} \times V_i = 1.80 \text{ M} \times 0.05 \text{ L}

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

Vi=1.80 M×0.05 L3.00 MV_i = \frac{1.80 \text{ M} \times 0.05 \text{ L}}{3.00 \text{ M}}

Simplifying the equation, we get:

Vi=0.09 L3.00 MV_i = \frac{0.09 \text{ L}}{3.00 \text{ M}}

Vi=0.03 LV_i = 0.03 \text{ L}

Now, we need to convert the volume from liters (L) to milliliters (mL):

Vi=0.03 L×1000 mL1 L=30.0 mLV_i = 0.03 \text{ L} \times \frac{1000 \text{ mL}}{1 \text{ L}} = 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 (mL) to liters (L) and plug in the values into the dilution formula. The student also needs to simplify the equation and solve for the unknown volume.

This problem is relevant to chemistry because it involves dilution, which is a crucial process in various applications, including laboratory experiments, industrial processes, and even everyday life. The student needs to understand the concept of dilution and how to apply the dilution formula to calculate the volume of a solution before and after dilution.

Key Concepts

  • Dilution formula: MiVi=MfVfM_i V_i = M_f V_f
  • Initial concentration: 3.00 M HCl
  • Final concentration: 1.80 M HCl
  • Initial volume: 0.003 L
  • Final volume: 0.05 L
  • Volume of 3.00 M HCl used: 30.0 mL
    A Student's Dilution Dilemma: Calculating the Volume of HCl ===========================================================

Q&A: Dilution and Concentration

Q: What is dilution?

A: Dilution is the process of reducing the concentration of a solution by adding a solvent. This process is essential in various applications, including laboratory experiments, industrial processes, and even everyday life.

Q: What is the dilution formula?

A: The dilution formula is given by:

MiVi=MfVfM_i V_i = M_f V_f

where:

  • MiM_i is the initial concentration of the solution (in moles per liter, M)
  • ViV_i is the initial volume of the solution (in liters, L)
  • MfM_f is the final concentration of the solution (in moles per liter, M)
  • VfV_f is the final volume of the solution (in liters, L)

Q: How do I calculate the volume of a solution before and after dilution?

A: To calculate the volume of a solution before and after dilution, you need to use the dilution formula. First, you need to convert the initial and final volumes from milliliters (mL) to liters (L). Then, you can plug in the values into the dilution formula and simplify the equation to solve for the unknown volume.

Q: What is the difference between initial and final concentration?

A: The initial concentration is the concentration of the solution before dilution, while the final concentration is the concentration of the solution after dilution.

Q: How do I convert milliliters (mL) to liters (L)?

A: To convert milliliters (mL) to liters (L), you can use the following conversion factor:

1 mL=0.001 L1 \text{ mL} = 0.001 \text{ L}

Q: What is the significance of dilution in chemistry?

A: Dilution is a crucial process in chemistry because it allows us to change the concentration of a solution without changing the amount of solute present. This process is essential in various applications, including laboratory experiments, industrial processes, and even everyday life.

Q: What are some common applications of dilution in chemistry?

A: Some common applications of dilution in chemistry include:

  • Preparing solutions for laboratory experiments
  • Diluting strong acids and bases
  • Preparing solutions for industrial processes
  • Preparing solutions for everyday use, such as cleaning products and personal care products

Q: What are some common mistakes to avoid when calculating dilution?

A: Some common mistakes to avoid when calculating dilution include:

  • Failing to convert milliliters (mL) to liters (L)
  • Failing to plug in the correct values into the dilution formula
  • Failing to simplify the equation correctly
  • Failing to solve for the unknown volume correctly

Conclusion

In this article, we have discussed the concept of dilution and how to calculate the volume of a solution before and after dilution using the dilution formula. We have also answered some common questions related to dilution and provided some tips and tricks for avoiding common mistakes. We hope that this article has been helpful in understanding the concept of dilution and how to apply it in various applications.

Key Concepts

  • Dilution formula: MiVi=MfVfM_i V_i = M_f V_f
  • Initial concentration: 3.00 M HCl
  • Final concentration: 1.80 M HCl
  • Initial volume: 0.003 L
  • Final volume: 0.05 L
  • Volume of 3.00 M HCl used: 30.0 mL
  • Conversion factor: 1 mL = 0.001 L