How Many Grams Of $CaCl_2$ Are In 250 ML Of $2.0 \, \text{M} \, CaCl_2$? $\square \, G \, CaCl_2$

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Understanding the Problem

To find the number of grams of $CaCl_2$ in 250 mL of $2.0 \, \text{M} \, CaCl_2$, we need to understand the concept of molarity and how it relates to the amount of substance in a given volume. Molarity is defined as the number of moles of solute per liter of solution. In this case, we have a 2.0 M solution of $CaCl_2$, which means there are 2.0 moles of $CaCl_2$ per liter of solution.

Calculating the Number of Moles of $CaCl_2$

To find the number of moles of $CaCl_2$ in 250 mL of solution, we need to first convert the volume from milliliters to liters. There are 1000 milliliters in 1 liter, so:

250 mL = 0.25 L

Now, we can use the molarity formula to find the number of moles of $CaCl_2$:

Molarity (M) = moles of solute / liters of solution

Rearranging the formula to solve for moles of solute, we get:

moles of solute = M x liters of solution

Substituting the values, we get:

moles of $CaCl_2$ = 2.0 M x 0.25 L = 0.5 moles

Calculating the Mass of $CaCl_2$

Now that we have the number of moles of $CaCl_2$, we can use the molar mass of $CaCl_2$ to find the mass of $CaCl_2$. The molar mass of $CaCl_2$ is 110.98 g/mol.

To find the mass of $CaCl_2$, we can multiply the number of moles by the molar mass:

mass of $CaCl_2$ = moles of $CaCl_2$ x molar mass of $CaCl_2$

Substituting the values, we get:

mass of $CaCl_2$ = 0.5 moles x 110.98 g/mol = 54.99 g

Conclusion

Therefore, there are approximately 54.99 grams of $CaCl_2$ in 250 mL of 2.0 M $CaCl_2$ solution.

Additional Information

To further understand the concept of molarity and how it relates to the amount of substance in a given volume, let's consider the following:

• Molarity is a measure of the concentration of a solution, expressed in units of moles per liter.
• The molarity of a solution can be calculated using the formula: M = moles of solute / liters of solution.
• The number of moles of solute in a given volume of solution can be calculated using the formula: moles of solute = M x liters of solution.
• The mass of solute in a given volume of solution can be calculated using the formula: mass of solute = moles of solute x molar mass of solute.

Example Problems

• What is the molarity of a solution that contains 3.5 moles of $NaCl$ in 2.5 L of solution?
• What is the mass of $NaCl$ in 1.5 L of 2.0 M $NaCl$ solution?
• What is the number of moles of $CaCl_2$ in 500 mL of 1.5 M $CaCl_2$ solution?

Solutions to Example Problems

• Molarity of solution = moles of solute / liters of solution = 3.5 moles / 2.5 L = 1.4 M
• Mass of $NaCl$ = moles of $NaCl$ x molar mass of $NaCl$ = 2.0 moles x 58.44 g/mol = 116.88 g
• Number of moles of $CaCl_2$ = M x liters of solution = 1.5 M x 0.5 L = 0.75 moles

Conclusion

In conclusion, the number of grams of $CaCl_2$ in 250 mL of 2.0 M $CaCl_2$ solution is approximately 54.99 grams. We can use the concept of molarity and the formulas for calculating the number of moles and mass of solute to solve problems involving the amount of substance in a given volume of solution.

Understanding Molarity and Concentration

Molarity is a measure of the concentration of a solution, expressed in units of moles per liter. It is an important concept in chemistry, as it allows us to calculate the amount of substance in a given volume of solution. In this article, we will answer some frequently asked questions about molarity and concentration of solutions.

Q: What is molarity?

A: Molarity is a measure of the concentration of a solution, expressed in units of moles per liter. It is defined as the number of moles of solute 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 solute and the volume of the solution in liters. The formula for molarity is:

M = moles of solute / liters of solution

Q: What is the difference between molarity and concentration?

A: Molarity is a measure of the concentration of a solution, expressed in units of moles per liter. Concentration, on the other hand, can be expressed in various units, such as mass per unit volume or volume per unit volume.

Q: How do I calculate the number of moles of solute in a given volume of solution?

A: To calculate the number of moles of solute in a given volume of solution, you need to know the molarity of the solution and the volume of the solution in liters. The formula for the number of moles of solute is:

moles of solute = M x liters of solution

Q: What is the mass of solute in a given volume of solution?

A: To calculate the mass of solute in a given volume of solution, you need to know the number of moles of solute and the molar mass of the solute. The formula for the mass of solute is:

mass of solute = moles of solute x molar mass of solute

Q: How do I convert between different units of concentration?

A: To convert between different units of concentration, you need to know the relationship between the units. For example, to convert from molarity to mass per unit volume, you need to know the molar mass of the solute.

Q: What is the significance of molarity in chemistry?

A: Molarity is an important concept in chemistry, as it allows us to calculate the amount of substance in a given volume of solution. It is used in a wide range of applications, including chemical reactions, stoichiometry, and chemical analysis.

Q: How do I determine the molarity of a solution if I only know the mass of solute and the volume of the solution?

A: To determine the molarity of a solution if you only know the mass of solute and the volume of the solution, you need to know the molar mass of the solute. You can then use the formula:

M = mass of solute / (molar mass of solute x volume of solution)

Q: What is the difference between a strong acid and a weak acid?

A: A strong acid is an acid that completely dissociates in water, producing a high concentration of hydrogen ions. A weak acid, on the other hand, only partially dissociates in water, producing a lower concentration of hydrogen ions.

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

A: To calculate the pH of a solution, you need to know the concentration of hydrogen ions in the solution. The pH is then calculated using the formula:

pH = -log[H+]

Q: What is the significance of pH in chemistry?

A: pH is an important concept in chemistry, as it allows us to determine the acidity or basicity of a solution. It is used in a wide range of applications, including chemical reactions, chemical analysis, and biological systems.

Conclusion

In conclusion, molarity and concentration of solutions are important concepts in chemistry. Understanding these concepts allows us to calculate the amount of substance in a given volume of solution and to determine the acidity or basicity of a solution. We hope that this article has provided a helpful overview of these concepts and has answered some of the frequently asked questions about molarity and concentration of solutions.