What Is The Concentration (in Mol $dm^{-3}$) Of A Solution Made By Dissolving 200 G Of $MgCl_2$ In Water And Making The Total Volume Up To $250 Cm^3$ Of Solution?

Understanding the Problem

To determine the concentration of a solution made by dissolving 200 g of magnesium chloride ($MgCl_2$) in water, we need to calculate the number of moles of $MgCl_2$ present in the solution and then divide it by the total volume of the solution in cubic decimeters ($dm^3$).

Calculating the Number of Moles of MgCl2

The molar mass of $MgCl_2$ is $58.33 g/mol$. To calculate the number of moles of $MgCl_2$ present in 200 g of the substance, we can use the following formula:

Number of moles = mass of substance / molar mass

Number of moles = 200 g / 58.33 g/mol = 3.43 mol

Calculating the Volume of the Solution in dm^3

The total volume of the solution is given as 250 cm^3. To convert this volume to cubic decimeters ($dm^3$), we can use the following conversion factor:

1 dm^3 = 1000 cm^3

Therefore, the volume of the solution in dm^3 is:

Volume = 250 cm^3 / 1000 = 0.25 dm^3

Calculating the Concentration of the Solution

The concentration of a solution is defined as the number of moles of solute present in a given volume of the solution. In this case, we have calculated the number of moles of $MgCl_2$ present in the solution and the total volume of the solution in dm^3. Therefore, we can calculate the concentration of the solution as follows:

Concentration = number of moles / volume of solution

Concentration = 3.43 mol / 0.25 dm^3 = 13.72 mol/dm^3

Conclusion

In this article, we have calculated the concentration of a solution made by dissolving 200 g of $MgCl_2$ in water and making the total volume up to 250 cm^3 of solution. We have used the formula for calculating the number of moles of a substance and the definition of concentration to arrive at the final answer.

Frequently Asked Questions

• What is the molar mass of $MgCl_2$?
  • The molar mass of $MgCl_2$ is 58.33 g/mol.
• How do I calculate the number of moles of a substance?
  • To calculate the number of moles of a substance, you can use the formula: number of moles = mass of substance / molar mass.
• What is the definition of concentration?
  • The concentration of a solution is defined as the number of moles of solute present in a given volume of the solution.

Step-by-Step Solution

1. Calculate the number of moles of $MgCl_2$ present in 200 g of the substance using the formula: number of moles = mass of substance / molar mass.
2. Convert the total volume of the solution from cm^3 to dm^3 using the conversion factor: 1 dm^3 = 1000 cm^3.
3. Calculate the concentration of the solution using the formula: concentration = number of moles / volume of solution.

Common Mistakes to Avoid

• Not converting the volume of the solution from cm^3 to dm^3.
• Not using the correct molar mass of $MgCl_2$.
• Not calculating the number of moles of $MgCl_2$ correctly.

Real-World Applications

The calculation of concentration is an important concept in chemistry and has many real-world applications. For example, in the pharmaceutical industry, the concentration of a solution is critical in determining the dosage of a medication. In the food industry, the concentration of a solution is important in determining the shelf life of a product. In the chemical industry, the concentration of a solution is critical in determining the yield of a reaction.

Conclusion

In conclusion, the concentration of a solution made by dissolving 200 g of $MgCl_2$ in water and making the total volume up to 250 cm^3 of solution is 13.72 mol/dm^3. This calculation is important in understanding the properties of a solution and has many real-world applications.

Q&A: Concentration of a Solution

Q1: What is the concentration of a solution made by dissolving 100 g of NaCl in water and making the total volume up to 200 cm^3 of solution?

A1: To calculate the concentration of the solution, we need to calculate the number of moles of NaCl present in 100 g of the substance and then divide it by the total volume of the solution in cubic decimeters (dm^3). The molar mass of NaCl is 58.44 g/mol. Therefore, the number of moles of NaCl present in 100 g of the substance is:

Number of moles = mass of substance / molar mass = 100 g / 58.44 g/mol = 1.71 mol

The total volume of the solution is given as 200 cm^3. To convert this volume to cubic decimeters (dm^3), we can use the following conversion factor:

1 dm^3 = 1000 cm^3

Therefore, the volume of the solution in dm^3 is:

Volume = 200 cm^3 / 1000 = 0.2 dm^3

The concentration of the solution is defined as the number of moles of solute present in a given volume of the solution. Therefore, we can calculate the concentration of the solution as follows:

Concentration = number of moles / volume of solution = 1.71 mol / 0.2 dm^3 = 8.55 mol/dm^3

Q2: What is the molar mass of MgCl2?

A2: The molar mass of MgCl2 is 58.33 g/mol.

Q3: How do I calculate the number of moles of a substance?

A3: To calculate the number of moles of a substance, you can use the formula: number of moles = mass of substance / molar mass.

Q4: What is the definition of concentration?

A4: The concentration of a solution is defined as the number of moles of solute present in a given volume of the solution.

Q5: How do I convert the volume of a solution from cm^3 to dm^3?

A5: To convert the volume of a solution from cm^3 to dm^3, you can use the following conversion factor: 1 dm^3 = 1000 cm^3.

Q6: What is the concentration of a solution made by dissolving 300 g of CaCl2 in water and making the total volume up to 300 cm^3 of solution?

A6: To calculate the concentration of the solution, we need to calculate the number of moles of CaCl2 present in 300 g of the substance and then divide it by the total volume of the solution in cubic decimeters (dm^3). The molar mass of CaCl2 is 110.98 g/mol. Therefore, the number of moles of CaCl2 present in 300 g of the substance is:

Number of moles = mass of substance / molar mass = 300 g / 110.98 g/mol = 2.70 mol

The total volume of the solution is given as 300 cm^3. To convert this volume to cubic decimeters (dm^3), we can use the following conversion factor:

1 dm^3 = 1000 cm^3

Therefore, the volume of the solution in dm^3 is:

Volume = 300 cm^3 / 1000 = 0.3 dm^3

The concentration of the solution is defined as the number of moles of solute present in a given volume of the solution. Therefore, we can calculate the concentration of the solution as follows:

Concentration = number of moles / volume of solution = 2.70 mol / 0.3 dm^3 = 9.00 mol/dm^3

Q7: What is the concentration of a solution made by dissolving 400 g of KCl in water and making the total volume up to 400 cm^3 of solution?

A7: To calculate the concentration of the solution, we need to calculate the number of moles of KCl present in 400 g of the substance and then divide it by the total volume of the solution in cubic decimeters (dm^3). The molar mass of KCl is 74.55 g/mol. Therefore, the number of moles of KCl present in 400 g of the substance is:

Number of moles = mass of substance / molar mass = 400 g / 74.55 g/mol = 5.37 mol

The total volume of the solution is given as 400 cm^3. To convert this volume to cubic decimeters (dm^3), we can use the following conversion factor:

1 dm^3 = 1000 cm^3

Therefore, the volume of the solution in dm^3 is:

Volume = 400 cm^3 / 1000 = 0.4 dm^3

The concentration of the solution is defined as the number of moles of solute present in a given volume of the solution. Therefore, we can calculate the concentration of the solution as follows:

Concentration = number of moles / volume of solution = 5.37 mol / 0.4 dm^3 = 13.43 mol/dm^3

Q8: What is the concentration of a solution made by dissolving 500 g of Na2SO4 in water and making the total volume up to 500 cm^3 of solution?

A8: To calculate the concentration of the solution, we need to calculate the number of moles of Na2SO4 present in 500 g of the substance and then divide it by the total volume of the solution in cubic decimeters (dm^3). The molar mass of Na2SO4 is 142.04 g/mol. Therefore, the number of moles of Na2SO4 present in 500 g of the substance is:

Number of moles = mass of substance / molar mass = 500 g / 142.04 g/mol = 3.52 mol

The total volume of the solution is given as 500 cm^3. To convert this volume to cubic decimeters (dm^3), we can use the following conversion factor:

1 dm^3 = 1000 cm^3

Therefore, the volume of the solution in dm^3 is:

Volume = 500 cm^3 / 1000 = 0.5 dm^3

The concentration of the solution is defined as the number of moles of solute present in a given volume of the solution. Therefore, we can calculate the concentration of the solution as follows:

Concentration = number of moles / volume of solution = 3.52 mol / 0.5 dm^3 = 7.04 mol/dm^3

Q9: What is the concentration of a solution made by dissolving 600 g of Ca(NO3)2 in water and making the total volume up to 600 cm^3 of solution?

A9: To calculate the concentration of the solution, we need to calculate the number of moles of Ca(NO3)2 present in 600 g of the substance and then divide it by the total volume of the solution in cubic decimeters (dm^3). The molar mass of Ca(NO3)2 is 164.10 g/mol. Therefore, the number of moles of Ca(NO3)2 present in 600 g of the substance is:

Number of moles = mass of substance / molar mass = 600 g / 164.10 g/mol = 3.65 mol

The total volume of the solution is given as 600 cm^3. To convert this volume to cubic decimeters (dm^3), we can use the following conversion factor:

1 dm^3 = 1000 cm^3

Therefore, the volume of the solution in dm^3 is:

Volume = 600 cm^3 / 1000 = 0.6 dm^3

The concentration of the solution is defined as the number of moles of solute present in a given volume of the solution. Therefore, we can calculate the concentration of the solution as follows:

Concentration = number of moles / volume of solution = 3.65 mol / 0.6 dm^3 = 6.08 mol/dm^3

Q10: What is the concentration of a solution made by dissolving 700 g of K2SO4 in water and making the total volume up to 700 cm^3 of solution?

A10: To calculate the concentration of the solution, we need to calculate the number of moles of K2SO4 present in 700 g of the substance and then divide it by the total volume of the solution in cubic decimeters (dm^3). The molar mass of K2SO4 is 174.26 g/mol. Therefore, the number of moles of K2SO4 present in 700 g of the substance is:

Number of moles = mass of substance / molar mass = 700 g / 174.26 g/mol = 4.02 mol

The total volume of the solution is given as 700 cm^3. To convert this volume to cubic decimeters (dm^3), we can use the following conversion factor:

1 dm^3 = 1000 cm^3

Therefore, the volume of the solution in dm^3 is:

Volume = 700 cm^3 / 1000 = 0.7 dm^3

The concentration