Question

You want to convert among molarity, molality, and mole fraction of a solution. You know the masses of solute and solvent and the volume of solution. Is this enough information to carry out all the conversions? Explain.

Short answer

Yes, the given information is sufficient to perform all the conversions.

Step-by-step solution

Calculating Molarity (M)

Molarity is defined as the number of moles of solute per liter of solution. To calculate molarity (\textbf{M}), use the formula: \[ M = \frac{{n_{\text{solute}}}}{{V_{\text{solution}}}} \] where: - \( n_{\text{solute}} \) is the number of moles of solute - \( V_{\text{solution}} \) is the volume of the solution in liters. Convert the given mass of solute to moles using its molar mass.

Calculating Molality (m)

Molality is defined as the number of moles of solute per kilogram of solvent. To calculate molality (\textbf{m}), use the formula: \[ m = \frac{{n_{\text{solute}}}}{{m_{\text{solvent}}}} \] where: - \( n_{\text{solute}} \) is the number of moles of solute - \( m_{\text{solvent}} \) is the mass of the solvent in kilograms. Convert the given mass of solvent to kilograms first.

Calculating Mole Fraction (\textbf{x})

Mole fraction is defined as the ratio of the number of moles of a component to the total number of moles in the solution. To calculate the mole fraction of the solute (\textbf{x_{\text{solute}}}), use the formula: \[ x_{\text{solute}} = \frac{{n_{\text{solute}}}}{{n_{\text{solute}} + n_{\text{solvent}}}} \] where: - \( n_{\text{solute}} \) is the number of moles of solute - \( n_{\text{solvent}} \) is the number of moles of solvent. Convert the given masses of solute and solvent to their respective moles using their molar masses.

Verify the Given Information

Ensure that you have all the necessary values: - Mass of solute and solvent for calculating the number of moles of each. - Volume of the solution for calculating molarity. With these pieces of information, you can carry out all the conversions.

Conclusion

Given the masses of solute and solvent and the volume of the solution, you have enough information to determine molarity, molality, and mole fraction of the solution.

Key concepts

Molarity calculation

Molarity is a way to express the concentration of a solution. It is defined as the number of moles of solute per liter of solution. To calculate molarity (\textbf{M}), you can use the formula: \[ M = \frac{n_{\text{solute}}}{V_{\text{solution}}} \] Here, \[ n_{\text{solute}} \] is the number of moles of solute, which you get by dividing the mass of the solute by its molar mass. \[ V_{\text{solution}} \] is the volume of the solution in liters (L). To put it simply:

• First, find the moles of the solute (\textbf{n}).
• Second, measure the volume of the solution in liters (L).
• Lastly, divide the moles of solute by the volume of solution.

By following these steps, you will get the molarity of the solution. Use this when you need to know how much solute is present in a certain amount of solution volume.

Molality calculation

Molality is another way to express the concentration of a solution, but it's slightly different from molarity. It's defined as the number of moles of solute per kilogram of solvent. To calculate molality (\textbf{m}), you use the formula: \[ m = \frac{n_{\text{solute}}}{m_{\text{solvent}}} \] Here, \[ n_{\text{solute}} \] is the number of moles of solute (the same as in molarity). \[ m_{\text{solvent}} \] is the mass of the solvent in kilograms (kg). Simple steps to follow:

• First, find the moles of the solute (\textbf{n}).
• Second, measure the mass of the solvent in kilograms (kg).
• Lastly, divide the moles of solute by the mass of the solvent.

Using these steps will give you the molality of the solution. Molality is particularly useful when the temperature of the solution changes, as it doesn't depend on volume.

Mole fraction calculation

Mole fraction is the ratio of the number of moles of a component to the total number of moles in the solution. To calculate the mole fraction of the solute (\textbf{x_{solute}}), you use the formula: \[ x_{\text{solute}} = \frac{n_{\text{solute}}}{n_{\text{solute}} + n_{\text{solvent}}} \] Here, both \[ n_{\text{solute}} \] and \[ n_{\text{solvent}} \] are the number of moles of the solute and solvent, respectively. Steps to follow:

• First, find the moles of the solute (\textbf{n_{solute}}).
• Second, find the moles of the solvent (\textbf{n_{solvent}}).
• Lastly, divide the moles of the solute by the total moles (solute + solvent).

This will give you the mole fraction of the solute. Remember, mole fraction does not have any unit, it's a dimensionless quantity.

Stoichiometry

Stoichiometry is the part of chemistry that deals with the relative quantities of reactants and products in chemical reactions. It helps to predict the amounts of substances consumed and produced. Important points in stoichiometry:

• Chemical Equation: A balanced chemical equation is essential.
• Molar Ratios: Use the coefficients in the balanced equation to find molar ratios.
• Calculations: Determine the moles of reactants or products to find how much is needed or produced.

For example, in a reaction: \[ aA + bB \rightarrow cC + dD \] The coefficients (a, b, c, d) tell you the molar ratios. So if you know the moles of A, you can find the moles of B needed and the moles of C and D produced. Stoichiometry connects the macroscopic world (grams, liters) with the microscopic world (atoms, molecules) using the concept of the mole.