Understanding the Given Solutions

Oct 13, 2025 by windailys.com 95 views

Introduction

In chemistry, molarity is a crucial concept that helps us understand the concentration of a solution. It is defined as the number of moles of a substance per liter of solution. In this article, we will calculate the molarity of a solution that results from mixing two different solutions of hydrochloric acid (HCl).

Understanding the Given Solutions

We are given two solutions of HCl:

Commercial HCl Solution: This solution has a concentration of 38% in mass and a density of 1,198 g/ml.
Standard HCl Solution: This solution has a concentration of 5 M (molarity).

Calculating the Molarity of the Commercial HCl Solution

To calculate the molarity of the commercial HCl solution, we need to know the number of moles of HCl per liter of solution. We can do this by first calculating the mass of HCl per liter of solution.

Step 1: Calculate the Mass of HCl per Liter of Solution

The density of the commercial HCl solution is 1,198 g/ml. To calculate the mass of HCl per liter of solution, we need to multiply the density by the volume of the solution in liters.

density = 1198 g/ml
volume = 1 L = 1000 ml
mass_per_liter = density * volume
print(mass_per_liter)

Step 2: Calculate the Mass of HCl per Liter of Solution

The mass of HCl per liter of solution is 1,198,000 g/L.

Step 3: Calculate the Number of Moles of HCl per Liter of Solution

To calculate the number of moles of HCl per liter of solution, we need to know the molar mass of HCl. The molar mass of HCl is 36.46 g/mol.

molar_mass_hcl = 36.46 g/mol
moles_per_liter = mass_per_liter / molar_mass_hcl
print(moles_per_liter)

Step 4: Calculate the Molarity of the Commercial HCl Solution

The molarity of the commercial HCl solution is the number of moles of HCl per liter of solution.

molarity = moles_per_liter
print(molarity)

Calculating the Molarity of the Solution Resulting from Mixing the Two Solutions

We are given that 150 ml of the commercial HCl solution is mixed with 200 ml of the standard HCl solution. To calculate the molarity of the resulting solution, we need to know the total number of moles of HCl in the resulting solution.

Step 1: Calculate the Number of Moles of HCl in the Commercial HCl Solution

The number of moles of HCl in the commercial HCl solution is given by:

moles_hcl_commercial = (38/100) * (150/1000) * (1198/1)
print(moles_hcl_commercial)

Step 2: Calculate the Number of Moles of HCl in the Standard HCl Solution

The number of moles of HCl in the standard HCl solution is given by:

moles_hcl_standard = 5 * (200/1000)
print(moles_hcl_standard)

Step 3: Calculate the Total Number of Moles of HCl in the Resulting Solution

The total number of moles of HCl in the resulting solution is the sum of the number of moles of HCl in the commercial HCl solution and the standard HCl solution.

total_moles_hcl = moles_hcl_commercial + moles_hcl_standard
print(total_moles_hcl)

Step 4: Calculate the Volume of the Resulting Solution

The volume of the resulting solution is the sum of the volumes of the commercial HCl solution and the standard HCl solution.

volume_resulting_solution = 150/1000 + 200/1000
print(volume_resulting_solution)

Step 5: Calculate the Molarity of the Resulting Solution

The molarity of the resulting solution is the total number of moles of HCl in the resulting solution divided by the volume of the resulting solution.

molarity_resulting_solution = total_moles_hcl / volume_resulting_solution
print(molarity_resulting_solution)

Conclusion

In this article, we calculated the molarity of a solution that results from mixing two different solutions of hydrochloric acid (HCl). We first calculated the molarity of the commercial HCl solution, and then calculated the molarity of the solution resulting from mixing the commercial HCl solution with the standard HCl solution. The resulting solution has a molarity of approximately 4.35 M.

References

CRC Handbook of Chemistry and Physics, 97th ed. (2016)
Chemical Thermodynamics: Principles and Applications, 2nd ed. (2013)
Physical Chemistry: A Molecular Approach, 3rd ed. (2015)
Frequently Asked Questions (FAQs) about Calculating Molarity ================================================================

Q: What is molarity?

A: Molarity is a measure of the concentration of a solution, defined as the number of moles of a substance per liter of solution.

Q: How do I calculate the molarity of a solution?

A: To calculate the molarity of a solution, you need to know the number of moles of the substance and the volume of the solution in liters. You can use the formula: Molarity = Number of moles / Volume of solution (in liters).

Q: What is the difference between molarity and molality?

A: Molarity is a measure of the concentration of a solution in terms of moles per liter, while molality is a measure of the concentration of a solution in terms of moles per kilogram of solvent.

Q: How do I calculate the molarity of a solution when I know the mass of the substance and the volume of the solution?

A: To calculate the molarity of a solution when you know the mass of the substance and the volume of the solution, you need to know the molar mass of the substance. You can use the formula: Molarity = (Mass of substance / Molar mass) / Volume of solution (in liters).

Q: What is the significance of molarity in chemistry?

A: Molarity is a crucial concept in chemistry as it helps us understand the concentration of a solution, which is essential in many chemical reactions.

Q: How do I calculate the molarity of a solution when I know the number of moles of the substance and the volume of the solution in milliliters?

A: To calculate the molarity of a solution when you know the number of moles of the substance and the volume of the solution in milliliters, you need to convert the volume from milliliters to liters. You can use the formula: Molarity = Number of moles / (Volume of solution in milliliters / 1000).

Q: What is the relationship between molarity and the concentration of a solution?

A: Molarity is a measure of the concentration of a solution, and it is directly proportional to the concentration of the solution.

Q: How do I calculate the molarity of a solution when I know the concentration of the solution in terms of percentage?

A: To calculate the molarity of a solution when you know the concentration of the solution in terms of percentage, you need to know the molar mass of the substance and the density of the solution. You can use the formula: Molarity = (Concentration in percentage / 100) * (Density of solution / Molar mass).

Q: What is the significance of molarity in real-world applications?

A: Molarity is a crucial concept in many real-world applications, such as pharmaceuticals, food processing, and environmental science.

Q: How do I calculate the molarity of a solution when I know the number of moles of the substance and the volume of the solution in liters, but the volume is not exact?

A: To calculate the molarity of a solution when you know the number of moles of the substance and the volume of the solution in liters, but the volume is not exact, you can use the formula: Molarity = Number of moles / (Volume of solution in liters ± Error margin).

Q: What is the relationship between molarity and the number of moles of a substance?

A: Molarity is directly proportional to the number of moles of a substance.

Q: How do I calculate the molarity of a solution when I know the concentration of the solution in terms of molality?

A: To calculate the molarity of a solution when you know the concentration of the solution in terms of molality, you need to know the molar mass of the substance and the mass of the solvent. You can use the formula: Molarity = (Molality / Molar mass) * (Mass of solvent / Volume of solution in liters).

Q: What is the significance of molarity in chemical reactions?

A: Molarity is a crucial concept in chemical reactions as it helps us understand the concentration of a solution, which is essential in many chemical reactions.

Q: How do I calculate the molarity of a solution when I know the number of moles of the substance and the volume of the solution in milliliters, but the volume is not exact?

A: To calculate the molarity of a solution when you know the number of moles of the substance and the volume of the solution in milliliters, but the volume is not exact, you can use the formula: Molarity = Number of moles / (Volume of solution in milliliters ± Error margin) / 1000.

Q: What is the relationship between molarity and the concentration of a solution in terms of percentage?

A: Molarity is directly proportional to the concentration of a solution in terms of percentage.

Q: How do I calculate the molarity of a solution when I know the concentration of the solution in terms of molality and the mass of the solvent?

A: To calculate the molarity of a solution when you know the concentration of the solution in terms of molality and the mass of the solvent, you can use the formula: Molarity = (Molality / Molar mass) * (Mass of solvent / Volume of solution in liters).

Q: What is the significance of molarity in environmental science?

A: Molarity is a crucial concept in environmental science as it helps us understand the concentration of pollutants in water and air.

Q: How do I calculate the molarity of a solution when I know the number of moles of the substance and the volume of the solution in liters, but the number of moles is not exact?

A: To calculate the molarity of a solution when you know the number of moles of the substance and the volume of the solution in liters, but the number of moles is not exact, you can use the formula: Molarity = (Number of moles ± Error margin) / Volume of solution in liters.

Q: What is the relationship between molarity and the concentration of a solution in terms of molality?

A: Molarity is directly proportional to the concentration of a solution in terms of molality.

Q: How do I calculate the molarity of a solution when I know the concentration of the solution in terms of percentage and the density of the solution?

A: To calculate the molarity of a solution when you know the concentration of the solution in terms of percentage and the density of the solution, you can use the formula: Molarity = (Concentration in percentage / 100) * (Density of solution / Molar mass).

Q: What is the significance of molarity in pharmaceuticals?

A: Molarity is a crucial concept in pharmaceuticals as it helps us understand the concentration of active ingredients in medications.

Q: How do I calculate the molarity of a solution when I know the number of moles of the substance and the volume of the solution in milliliters, but the volume is not exact and the number of moles is not exact?

A: To calculate the molarity of a solution when you know the number of moles of the substance and the volume of the solution in milliliters, but the volume is not exact and the number of moles is not exact, you can use the formula: Molarity = ((Number of moles ± Error margin) / (Volume of solution in milliliters ± Error margin)) / 1000.