Which Equation Shows The Proper Setup To Find The Volume Of A $0.250 \, M \, \text{CaCl}_2$ Solution That Contains $39.5 \, G$ Of $\text{CaCl}_2$?A. $0.250 \, M \, \text{CaCl}_2 = \frac{39.5 \, G \,

Understanding the Problem

To find the volume of a solution, we need to know the concentration of the solution, the mass of the solute, and the molar mass of the solute. In this problem, we are given a $0.250 \, M \, \text{CaCl}_2$ solution that contains $39.5 \, g$ of $\text{CaCl}_2$. We need to find the volume of the solution.

Calculating the Number of Moles of CaCl2

To find the volume of the solution, we first need to calculate the number of moles of $\text{CaCl}_2$. We can do this by dividing the mass of $\text{CaCl}_2$ by its molar mass.

The molar mass of $\text{CaCl}_2$ is $110.98 \, g/mol$. We can calculate the number of moles of $\text{CaCl}_2$ as follows:

$$\text{Number of moles of CaCl}_2 = \frac{\text{Mass of CaCl}_2}{\text{Molar mass of CaCl}_2}$$

$$\text{Number of moles of CaCl}_2 = \frac{39.5 \, g}{110.98 \, g/mol}$$

$$\text{Number of moles of CaCl}_2 = 0.356 \, mol$$

Calculating the Volume of the Solution

Now that we have the number of moles of $\text{CaCl}_2$, we can calculate the volume of the solution. We can do this by dividing the number of moles of $\text{CaCl}_2$ by its molarity.

The molarity of the solution is $0.250 \, M$. We can calculate the volume of the solution as follows:

$$\text{Volume of the solution} = \frac{\text{Number of moles of CaCl}_2}{\text{Molarity of the solution}}$$

$$\text{Volume of the solution} = \frac{0.356 \, mol}{0.250 \, M}$$

$$\text{Volume of the solution} = 1.424 \, L$$

Choosing the Correct Equation

Now that we have calculated the volume of the solution, we can choose the correct equation to represent this calculation. The correct equation is:

$$\text{Volume of the solution} = \frac{\text{Number of moles of CaCl}_2}{\text{Molarity of the solution}}$$

$$\text{Volume of the solution} = \frac{0.356 \, mol}{0.250 \, M}$$

$$\text{Volume of the solution} = 1.424 \, L$$

This equation shows the proper setup to find the volume of a $0.250 \, M \, \text{CaCl}_2$ solution that contains $39.5 \, g$ of $\text{CaCl}_2$.

Conclusion

In conclusion, to find the volume of a solution, we need to know the concentration of the solution, the mass of the solute, and the molar mass of the solute. We can calculate the number of moles of the solute by dividing the mass of the solute by its molar mass. We can then calculate the volume of the solution by dividing the number of moles of the solute by its molarity. The correct equation to represent this calculation is:

$$\text{Volume of the solution} = \frac{\text{Number of moles of CaCl}_2}{\text{Molarity of the solution}}$$

$$\text{Volume of the solution} = \frac{0.356 \, mol}{0.250 \, M}$$

$$\text{Volume of the solution} = 1.424 \, L$$

This equation shows the proper setup to find the volume of a $0.250 \, M \, \text{CaCl}_2$ solution that contains $39.5 \, g$ of $\text{CaCl}_2$.

Equation Options

Let's examine the equation options provided:

A. $0.250 \, M \, \text{CaCl}_2 = \frac{39.5 \, g}{110.98 \, g/mol}$

This equation is incorrect because it does not take into account the molarity of the solution.

B. $0.250 \, M \, \text{CaCl}_2 = \frac{39.5 \, g}{0.250 \, M}$

This equation is incorrect because it does not take into account the molar mass of the solute.

C. $0.250 \, M \, \text{CaCl}_2 = \frac{39.5 \, g}{110.98 \, g/mol} \div 0.250 \, M$

This equation is incorrect because it does not represent the correct calculation for the volume of the solution.

D. $0.250 \, M \, \text{CaCl}_2 = \frac{39.5 \, g}{110.98 \, g/mol} \div \frac{1}{0.250 \, M}$

This equation is correct because it represents the correct calculation for the volume of the solution.

Conclusion

In conclusion, the correct equation to find the volume of a $0.250 \, M \, \text{CaCl}_2$ solution that contains $39.5 \, g$ of $\text{CaCl}_2$ is:

$$\text{Volume of the solution} = \frac{\text{Number of moles of CaCl}_2}{\text{Molarity of the solution}}$$

$$\text{Volume of the solution} = \frac{0.356 \, mol}{0.250 \, M}$$

$$\text{Volume of the solution} = 1.424 \, L$$

This equation shows the proper setup to find the volume of a $0.250 \, M \, \text{CaCl}_2$ solution that contains $39.5 \, g$ of $\text{CaCl}_2$.

Q: What is the formula to find the volume of a solution?

A: The formula to find the volume of a solution is:

$$\text{Volume of the solution} = \frac{\text{Number of moles of solute}}{\text{Molarity of the solution}}$$

Q: What is the molarity of a solution?

A: The molarity of a solution is the number of moles of solute per liter of solution. It is typically expressed in units of moles per liter (M).

Q: How do I calculate the number of moles of a solute?

A: To calculate the number of moles of a solute, you need to know the mass of the solute and its molar mass. The molar mass is the mass of one mole of the solute. You can calculate the number of moles of a solute using the following formula:

$$\text{Number of moles of solute} = \frac{\text{Mass of solute}}{\text{Molar mass of solute}}$$

Q: What is the difference between molarity and molality?

A: Molarity and molality are both measures of concentration, but they are defined differently. Molarity is the number of moles of solute per liter of solution, while molality is the number of moles of solute per kilogram of solvent.

Q: How do I convert between molarity and molality?

A: To convert between molarity and molality, you need to know the density of the solution. The density of the solution is the mass of the solution per unit volume. You can use the following formula to convert between molarity and molality:

$$\text{Molarity} = \frac{\text{Molality} \times \text{Density of solution}}{1000}$$

Q: What is the significance of the molar mass of a solute?

A: The molar mass of a solute is the mass of one mole of the solute. It is an important property of a solute because it determines the number of moles of the solute that can be dissolved in a given volume of solution.

Q: How do I calculate the volume of a solution using the molar mass of a solute?

A: To calculate the volume of a solution using the molar mass of a solute, you need to know the number of moles of the solute and its molar mass. You can use the following formula to calculate the volume of a solution:

$$\text{Volume of solution} = \frac{\text{Number of moles of solute} \times \text{Molar mass of solute}}{\text{Molarity of solution}}$$

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

A: The volume of a solution is inversely proportional to its concentration. This means that as the concentration of a solution increases, its volume decreases.

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

A: To calculate the concentration of a solution, you need to know the number of moles of the solute and the volume of the solution. You can use the following formula to calculate the concentration of a solution:

$$\text{Concentration of solution} = \frac{\text{Number of moles of solute}}{\text{Volume of solution}}$$

Q: What is the significance of the density of a solution?

A: The density of a solution is the mass of the solution per unit volume. It is an important property of a solution because it determines its concentration.

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

A: To calculate the density of a solution, you need to know the mass of the solution and its volume. You can use the following formula to calculate the density of a solution:

$$\text{Density of solution} = \frac{\text{Mass of solution}}{\text{Volume of solution}}$$

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

A: The density of a solution is directly proportional to its concentration. This means that as the concentration of a solution increases, its density also increases.

Q: How do I calculate the concentration of a solution using its density?

A: To calculate the concentration of a solution using its density, you need to know the density of the solution and its molar mass. You can use the following formula to calculate the concentration of a solution:

$$\text{Concentration of solution} = \frac{\text{Density of solution} \times \text{Molar mass of solute}}{1000}$$

Q: What is the significance of the molar mass of a solvent?

A: The molar mass of a solvent is the mass of one mole of the solvent. It is an important property of a solvent because it determines the number of moles of the solvent that can be dissolved in a given volume of solution.

Q: How do I calculate the volume of a solution using the molar mass of a solvent?

A: To calculate the volume of a solution using the molar mass of a solvent, you need to know the number of moles of the solvent and its molar mass. You can use the following formula to calculate the volume of a solution:

$$\text{Volume of solution} = \frac{\text{Number of moles of solvent} \times \text{Molar mass of solvent}}{\text{Molarity of solution}}$$

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

A: The volume of a solution is inversely proportional to its concentration. This means that as the concentration of a solution increases, its volume decreases.

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

A: To calculate the concentration of a solution, you need to know the number of moles of the solute and the volume of the solution. You can use the following formula to calculate the concentration of a solution:

$$\text{Concentration of solution} = \frac{\text{Number of moles of solute}}{\text{Volume of solution}}$$

Q: What is the significance of the density of a solution?

A: The density of a solution is the mass of the solution per unit volume. It is an important property of a solution because it determines its concentration.

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

A: To calculate the density of a solution, you need to know the mass of the solution and its volume. You can use the following formula to calculate the density of a solution:

$$\text{Density of solution} = \frac{\text{Mass of solution}}{\text{Volume of solution}}$$

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

A: The density of a solution is directly proportional to its concentration. This means that as the concentration of a solution increases, its density also increases.

Q: How do I calculate the concentration of a solution using its density?

A: To calculate the concentration of a solution using its density, you need to know the density of the solution and its molar mass. You can use the following formula to calculate the concentration of a solution:

$$\text{Concentration of solution} = \frac{\text{Density of solution} \times \text{Molar mass of solute}}{1000}$$

Q: What is the significance of the molar mass of a solute?

A: The molar mass of a solute is the mass of one mole of the solute. It is an important property of a solute because it determines the number of moles of the solute that can be dissolved in a given volume of solution.

Q: How do I calculate the volume of a solution using the molar mass of a solute?

A: To calculate the volume of a solution using the molar mass of a solute, you need to know the number of moles of the solute and its molar mass. You can use the following formula to calculate the volume of a solution:

$$\text{Volume of solution} = \frac{\text{Number of moles of solute} \times \text{Molar mass of solute}}{\text{Molarity of solution}}$$

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

A: The volume of a solution is inversely proportional to its concentration. This means that as the concentration of a solution increases, its volume decreases.

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

A: To calculate the concentration of a solution, you need to know the number of moles of the solute and the volume of the solution. You can use the following formula to calculate the concentration of a solution:

$$\text{Concentration of solution} = \frac{\text{Number of moles of solute}}{\text{Volume of solution}}$$

Q: What is the significance of the density of a solution?

A: The density of a solution is the mass of the solution per unit volume. It is an important property of a solution because it determines its concentration.

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

A: To calculate the density of a solution, you need to know the mass of the solution and its volume. You can use the following formula to calculate the density of a solution:

\text{Density of solution