Question

Calculate the volume of a \(0.156 \mathrm{M} \mathrm{CuSO}_{4}\) solution that would react with \(7.89 \mathrm{~g}\) of zinc.

Short answer

773 mL of the 0.156 M CuSO4 solution is needed.

Step-by-step solution

Write the Balanced Chemical Equation

First, identify the chemical reaction between zinc (Zn) and copper(II) sulfate (\( ext{CuSO}_4 \). This is a single displacement reaction and can be written as:\[ ext{Zn} + ext{CuSO}_{4} \rightarrow ext{ZnSO}_{4} + ext{Cu}\]This equation is balanced as written; one atom of Zn reacts with one molecule of \(\text{CuSO}_4\).

Calculate Moles of Zinc

Next, convert the mass of zinc to moles using its molar mass. The molar mass of Zn is approximately 65.38 g/mol.\(\text{Moles of Zn} = \frac{7.89 \, \text{g}}{65.38 \, \text{g/mol}} \approx 0.1207 \, \text{moles}\)

Determine Moles of CuSO4 Required

From the balanced equation, 1 mole of Zn reacts with 1 mole of \(\text{CuSO}_4\). Therefore, 0.1207 moles of Zn will require 0.1207 moles of \(\text{CuSO}_4\).

Calculate Volume of CuSO4 Solution

Now, use the concentration of the \(\text{CuSO}_4\) solution to find the required volume. The concentration is given as 0.156 M, which means 0.156 moles per liter.Using the formula\[\text{Volume} = \frac{\text{Moles of } \text{CuSO}_4}{\text{Concentration}} = \frac{0.1207 \, \text{moles}}{0.156 \, \text{M}} \approx 0.773 \, \text{liters}\]

Final Step: Convert to Milliliters

Finally, convert the volume from liters to milliliters:\(0.773 \, \text{liters} \times 1000 \, \frac{\text{mL}}{\text{liter}} = 773 \, \text{mL}\)

Key concepts

Molar Concentration

Molar concentration describes the number of moles of a solute in one liter of solution. It is expressed in moles per liter (mol/L) or simply as M for molarity. Understanding molarity is essential for performing stoichiometric calculations in chemistry.
For example, in the reaction involving copper(II) sulfate (CuSO₄) and zinc (Zn), we know that the molar concentration of the CuSO₄ solution is 0.156 M. This means there are 0.156 moles of CuSO₄ in every liter of solution.

• This allows us to calculate how many moles are present in a given volume of solution.
• It is crucial when figuring out how much reactant is needed or produced in a chemical reaction.

Always ensure that your units match when performing calculations involving molarity.

Chemical Reactions

Chemical reactions occur when substances interact to form new products. In our exercise, zinc (Zn) reacts with copper(II) sulfate (CuSO₄) in a single displacement reaction.
The balanced chemical equation for this reaction is:
\[\text{Zn} + \text{CuSO}_4 \rightarrow \text{ZnSO}_4 + \text{Cu}\]Balanced equations are vital as they indicate the proportion of reactants and products. Here are some basics about this type of chemical reaction:

• A balanced reaction respects the law of conservation of mass, meaning the number of atoms for each element is the same on both sides of the equation.
• Single displacement reactions involve one element being replaced by another in a compound.

Understanding the balanced equation helps us determine how chemicals interact and the amounts needed for reactions to occur.

Molar Mass

Molar mass is the mass of one mole of a substance, usually expressed in grams per mole (g/mol). It serves as a bridge between the mass of a substance and the amount in moles.
Take zinc (Zn) as an example; its molar mass is approximately 65.38 g/mol. This means that one mole of zinc weighs 65.38 grams.

• To convert a given mass to moles, divide the mass by the molar mass.
• In our problem, the conversion of 7.89 g of zinc is accomplished by dividing by its molar mass, leading to approximately 0.1207 moles of zinc.

Molar mass is fundamental in stoichiometry as it allows for the conversion between grams and moles, enabling accurate calculations in chemical equations.

Solution Volume

Solution volume is the amount of space that a solution occupies, typically measured in liters or milliliters. Calculating the volume required for a reaction is a common task in chemistry.
In the CuSO₄ and Zn reaction, we needed to find the volume of CuSO₄ solution that contains 0.1207 moles of solute given a molarity of 0.156 M.
You can determine the volume with the formula:
\[\text{Volume} = \frac{\text{Moles of solute}}{\text{Molarity}}\]

• In this case, dividing the 0.1207 moles of CuSO₄ by the 0.156 M molarity gives a volume of approximately 0.773 liters.
• Converting to milliliters by multiplying by 1000 results in 773 mL.

Proper calculation of solution volume ensures the right amount of reactant is used, impacting the outcome of chemical experiments.