Problem 62 - Chemistry: The Central Science in SI Units, Global Edition

Question

(a) Calculate the molarity of a solution made by dissolving 12.5 grams of \(\mathrm{Na}_{2} \mathrm{CrO}_{4}\) in enough water to form exactly \(750 \mathrm{~mL}\) of solution. (b) How many moles of KBr are present in \(150 \mathrm{~mL}\) of a \(0.112 \mathrm{M}\) solution? (c) How many milliliters of \(6.1 \mathrm{MHCl}\) colution a

Step-by-Step Solution

Answer

To summarize: a) The molarity of the Na₂CrO₄ solution is 0.103 M. b) There are 0.0168 moles of KBr in 150 mL of a 0.112 M solution. c) Part (c) of the question is incomplete and we need more information for a proper solution.

Step 1: Part A: Calculate the molarity of Na2CrO4 solution

1. Calculate the molar mass of Na2CrO4: The molar mass of Na₂CrO₄ can be found by calculating the sum of the molar masses of its individual elements:$$ \mathrm{Na}_{2} \mathrm{CrO}_{4}=2(\mathrm{Na})+\mathrm{Cr}+4(\mathrm{O}) $$Use the atomic masses from the periodic table to find the molar mass of each element:$$ \mathrm{Na} = 22.99\,\mathrm{g/mol} $$ \mathrm{Cr} = 51.996\,\mathrm{g/mol} $$ \mathrm{O} = 16\,\mathrm{g/mol} $$Plug the values into the formula and find the molar mass of Na₂CrO₄:$$ 2(22.99\,\mathrm{g/mol}) + 51.996\,\mathrm{g/mol} + 4(16\,\mathrm{g/mol}) = 161.97\,\mathrm{g/mol} $$2. Convert the mass of Na₂CrO₄ to moles: Now that we have the molar mass, we can convert the given mass (12.5 g) of Na₂CrO₄ to moles:$$ \frac{12.5\,\mathrm{g}}{161.97\,\mathrm{g/mol}}=0.0772\,\mathrm{mol} $$3. Convert volume to liters: Given that the solution has a volume of 750 mL, we need to convert this to liters for the molarity calculation:$$ 750\,\mathrm{mL} \times \frac{1\,\mathrm{L}}{1000\,\mathrm{mL}}=0.750\,\mathrm{L} $$4. Calculate the molarity of the Na₂CrO₄ solution: Plug the values of moles and volume in liters into the molarity formula:$$ M = \frac{n}{V} = \frac{0.0772\,\mathrm{mol}}{0.750\,\mathrm{L}}=0.103\,\mathrm{M} $$Therefore, the molarity of the Na₂CrO₄ solution is 0.103 M.

Step 2: Part B: Determine the number of moles in a 0.112M KBr solution

1. Convert the volume to liters: The given volume of the KBr solution is 150 mL. Convert it to liters:$$ 150\,\mathrm{mL} \times \frac{1\,\mathrm{L}}{1000\,\mathrm{mL}}=0.150\,\mathrm{L} $$2. Calculate the moles of KBr: Given that the molarity of the KBr solution is 0.112 M, use the molarity formula to find the number of moles in the solution:$$ n= M \times V=0.112\,\mathrm{M} \times 0.150\,\mathrm{L} = 0.0168\,\mathrm{mol} $$Therefore, there are 0.0168 moles of KBr in 150 mL of a 0.112 M solution.

Step 3: Part C: Calculate the volume of a 6.1M HCl solution

It appears that the exercise is incomplete after part (c) because the required volume or moles of HCl are not given. Please provide more information about part (c) to receive a complete solution.

Key Concepts

Molar Mass Calculation

Calculating the molar mass is a fundamental step in finding the molarity of a solution. Molar mass refers to the mass of one mole of a substance, expressed in grams per mole (g/mol). It is derived from the atomic masses of the elements, which can be found on the periodic table.

For example, in the molecule \(\text{Na}_2\text{CrO}_4\), the molar mass can be calculated by adding together the masses of 2 sodium (Na) atoms, 1 chromium (Cr) atom, and 4 oxygen (O) atoms.

• The atomic mass of sodium (Na) is 22.99 g/mol.
• The atomic mass of chromium (Cr) is 51.996 g/mol.
• The atomic mass of oxygen (O) is 16 g/mol.

Summing these up gives you the total molar mass: \(2 \times 22.99 + 51.996 + 4 \times 16 = 161.97 \text{ g/mol}\).

With the molar mass known, you can convert any given mass of the compound to moles, setting the stage for further calculations like determining molarity.

Conversion of Units

When working with molarity and solution concentration, unit conversions are essential to ensure all quantities are compatible. Typically, to calculate molarity, the volume should be expressed in liters (L), which is the standard unit in molarity calculations.

For instance, if you have a solution volume given in milliliters (mL), convert it to liters by using the conversion factor: \(1 \text{ L} = 1000 \text{ mL}\). So, an amount such as 750 mL can be converted as follows: \(750 \text{ mL} \times \frac{1 \text{ L}}{1000 \text{ mL}} = 0.750 \text{ L}\).

This conversion is crucial because molarity is defined as moles of solute per liter of solution (mol/L). Therefore, ensuring the volume is in liters simplifies the molarity calculation and aligns with standard scientific practices.

Solution Preparation

Preparing a solution with a specific molarity involves careful measurement of both the solute and the solvent. It begins by calculating the number of moles needed for the desired molarity using the formula: \(M = \frac{n}{V}\), where \(M\) is the molarity, \(n\) is the moles of solute, and \(V\) is the volume of the solution in liters.

For example, if you need a certain molarity, first determine the moles of solute needed and then dissolve this calculated amount of the solute in enough solvent to reach the desired total volume of solution.

Let's say you have 12.5 grams of \(\text{Na}_2\text{CrO}_4\) and need to make a solution with a known molarity. First, calculate moles from grams using the molar mass (as discussed earlier): \(\frac{12.5 \text{ g}}{161.97 \text{ g/mol}} = 0.0772 \text{ mol}\). Then, decide on the total solution volume and use the molarity formula to determine the final setup.

• Carefully dissolve the solute in a portion of the solvent.
• Adjust the final volume to the desired level with more solvent.

This step-by-step method ensures accuracy and consistency in preparing chemical solutions.