Problem 62 - Chemistry The Central Science In Si Units

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 \(\mathrm{KBr}\) are present in \(150 \mathrm{~mL}\) of a \(0.112 \mathrm{M}\) solution? (c) How many milliliters of \(6.1 \mathrm{MHCl}\) solution are needed to obtain 0.150 mol of HCl?

Step-by-Step Solution

Answer

(a) 0.1028 M (b) 0.0168 mol (c) 24.59 mL

Step 1: Determine the molar mass of Na2CrO4

Find the molar mass of Na2CrO4 by adding the atomic masses of all its atoms.\[ \text{Na: } 23.0 \text{ g/mol} \times 2 = 46.0 \text{ g/mol}, \]\[ \text{Cr: } 51.9961 \text{ g/mol}, \]\[ \text{O: } 16.0 \text{ g/mol} \times 4 = 64.0 \text{ g/mol}. \]Thus, \[ \text{Molar mass of } \mathrm{Na}_2\mathrm{CrO}_4 = 46.0 + 51.9961 + 64.0 = 161.9961 \text{ g/mol}. \]

Step 2: Calculate moles of Na2CrO4

Divide the given mass of Na2CrO4 by its molar mass to get the moles.\[ \text{Moles of } \mathrm{Na}_2\mathrm{CrO}_4 = \frac{12.5 \text{ g}}{161.9961 \text{ g/mol}} \approx 0.0771 \text{ mol}. \]

Step 3: Calculate the molarity of Na2CrO4

Molarity is defined as the number of moles of solute per liter of solution. Convert 750 mL to liters: 750 mL = 0.750 L.\[ \text{Molarity} = \frac{0.0771 \text{ mol}}{0.750 \text{ L}} \approx 0.1028 \text{ M}. \]

Step 4: Calculate moles of KBr

Use the given molarity of the KBr solution to find moles by multiplying the molarity with the volume in liters.\[ V = 150 \text{ mL} = 0.150 \text{ L}. \]\[ \text{Moles of KBr} = 0.112 \text{ M} \times 0.150 \text{ L} = 0.0168 \text{ mol}. \]

Step 5: Calculate volume of HCl needed

To find the volume of HCl solution needed to obtain 0.150 mol HCl, use the formula: Volume (L) = moles/molarity.\[ \text{Volume of HCl} = \frac{0.150 \text{ mol}}{6.1 \text{ M}} = 0.02459 \text{ L} \approx 24.59 \text{ mL}. \]

Key Concepts

Molar Mass

Molar mass is a fundamental concept in chemistry that helps us understand the relationship between the mass of a substance and the amount of it in moles. It is expressed in units of grams per mole (g/mol). Molar mass can be calculated by summing the atomic masses of all atoms in a given molecule or compound.

For example, in the original exercise, we calculated the molar mass of sodium chromate (\(\mathrm{Na}_2\mathrm{CrO}_4\)) by adding up the atomic masses of sodium (Na), chromium (Cr), and oxygen (O). Each element's atomic mass is found on the periodic table of elements:

• Na: 23.0 g/mol (multiplied by 2 because there are two sodium atoms)
• Cr: 51.9961 g/mol
• O: 16.0 g/mol (multiplied by 4 because there are four oxygen atoms)

Adding these values gives us the total molar mass: \[ 46.0 + 51.9961 + 64.0 = 161.9961 \text{ g/mol}. \]Understanding and calculating the molar mass is crucial for various chemical calculations, including determining the number of moles in a given sample.

Moles

Moles, often represented as \(\text{mol}\), are a unit of measurement in chemistry that describe the quantity of substance. One mole contains exactly \(6.022 \times 10^{23}\) particles (atoms, molecules, ions, etc.). This number is known as Avogadro's number.

To find the number of moles from a specific mass of a substance, you use the formula:
\[ \text{Moles} = \frac{\text{Mass (g)}}{\text{Molar Mass (g/mol)}}. \]
In the given exercise, we calculated the moles of sodium chromate by dividing its mass (12.5 g) by its molar mass (161.9961 g/mol):
\[ \text{Moles of } \mathrm{Na}_2\mathrm{CrO}_4 = \frac{12.5 \text{ g}}{161.9961 \text{ g/mol}} \approx 0.0771 \text{ mol}. \]
This relationship allows chemists to convert between the mass of a substance and the number of moles, facilitating stoichiometric calculations and reaction predictions.

Solution Concentration

Solution concentration, often referred to by chemists as molarity (\(M\)), describes the amount of solute dissolved in a given volume of solution. It is expressed in moles per liter (mol/L). Knowing the concentration of a solution is essential for preparing solutions for reactions and for analyzing the products of those reactions.

The formula for molarity is:
\[ \text{Molarity} (M) = \frac{\text{moles of solute}}{\text{volume of solution in liters}}. \]
In the exercise, we used this formula to calculate the concentration of \(\mathrm{Na}_2\mathrm{CrO}_4\) in a solution made by dissolving 12.5 grams of the substance in 750 mL (0.750 L) of water. The molarity was found by dividing the moles (0.0771 mol) by the volume in liters:
\[ \text{Molarity} = \frac{0.0771 \text{ mol}}{0.750 \text{ L}} \approx 0.1028 \text{ M}. \]
Understanding this calculation helps in creating specific concentrations necessary for laboratory work and various chemical processes.

Chemical Calculations

Chemical calculations involve using known values (such as molarity, volume, and moles) to determine unknown aspects of a chemical reaction or preparation. They require a systematic approach, often employing formulas and conversions.

In the exercise, several chemical calculations were performed:

• Moles of \(\mathrm{KBr}\) in a 150 mL (0.150 L) solution with a known molarity of 0.112 M. Using the formula \(\text{Moles} = \text{Molarity} \times \text{Volume (L)}\), we calculate:
  \[ \text{Moles of KBr} = 0.112 \text{ M} \times 0.150 \text{ L} = 0.0168 \text{ mol}. \]
• Volume of \(6.1 \text{ M} \mathrm{HCl}\) solution needed to provide 0.150 mol of \(\mathrm{HCl}\). We rearrange the formula to \(\text{Volume (L)} = \frac{\text{moles}}{\text{molarity}}\):
  \[ \text{Volume of HCl} = \frac{0.150 \text{ mol}}{6.1 \text{ M}} \approx 0.02459 \text{ L} \approx 24.59 \text{ mL}. \]

These calculations are pivotal in laboratory settings to ensure precise measurement and formulation of solutions needed for chemical reactions and experiments.