Question

Calculate the molarity of each aqueous solution: (a) \(0.82 \mathrm{~g}\) of ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)\) in \(10.5 \mathrm{~mL}\) of solution (b) \(1.27 \mathrm{~g}\) of gaseous \(\mathrm{NH}_{3}\) in \(33.5 \mathrm{~mL}\) of solution

Short answer

(a) The molarity of the ethanol solution is 1.70 M. (b) The molarity of the ammonia solution is 2.22 M.

Step-by-step solution

Understand the Concept of Molarity

Molarity is a measure of the concentration of a solute in a solution, expressed as the number of moles of solute per liter of solution. It is represented by the formula: \[ M = \frac{n}{V} \] where \(M\) is the molarity, \(n\) is the number of moles of solute, and \(V\) is the volume of the solution in liters.

Calculate Moles of Ethanol (Part a)

1. Find the molar mass of ethanol (\( \text{C}_2 \text{H}_5 \text{OH} \)): \[ 2 \times 12.01 + 6 \times 1.01 + 16.00 = 46.08 \text{ g/mol} \] 2. Determine the number of moles of ethanol using the mass provided: \[ n = \frac{0.82 \text{ g}}{46.08 \text{ g/mol}} = 0.0178 \text{ moles} \]

Convert Volume to Liters (Part a)

Convert the volume of the solution from milliliters to liters: \[ V = \frac{10.5 \text{ mL}}{1000} = 0.0105 \text{ L} \]

Calculate Molarity of Ethanol Solution (Part a)

Use the molarity formula: \[ M = \frac{n}{V} = \frac{0.0178 \text{ moles}}{0.0105 \text{ L}} = 1.70 \text{ M} \]

Calculate Moles of Ammonia (Part b)

1. Find the molar mass of ammonia (\( \text{NH}_3 \)): \[ 1 \times 14.01 + 3 \times 1.01 = 17.04 \text{ g/mol} \] 2. Determine the number of moles of ammonia using the mass provided: \[ n = \frac{1.27 \text{ g}}{17.04 \text{ g/mol}} = 0.0745 \text{ moles} \]

Convert Volume to Liters (Part b)

Convert the volume of the solution from milliliters to liters: \[ V = \frac{33.5 \text{ mL}}{1000} = 0.0335 \text{ L} \]

Calculate Molarity of Ammonia Solution (Part b)

Use the molarity formula: \[ M = \frac{n}{V} = \frac{0.0745 \text{ moles}}{0.0335 \text{ L}} = 2.22 \text{ M} \]

Key concepts

Molarity Calculation Explained

Understanding molarity is crucial in solution chemistry. Molarity, denoted as \( M \), measures the concentration of a solute in a solution. It is defined as the number of moles of solute per liter of solution. The formula is simple yet powerful: \[ M = \frac{n}{V} \] where \( n \) represents the number of moles of the solute, and \( V \) denotes the volume of the solution in liters. This unit, molarity, helps us understand how concentrated a solution is, which is essential in various chemical experiments.

Ethanol in Solution Chemistry

Ethanol, often represented as \( \text{C}_2 \text{H}_5 \text{OH} \), is a common organic compound used in various chemical solutions. To determine its molarity, we first need to understand the molar mass of ethanol. Ethanol has: \[ 2 \text{ Carbons} \times 12.01 + 6 \text{ Hydrogens} \times 1.01 + 1 \text{ Oxygen} \times 16.00 = 46.08 \text{ g/mol} \] Using this molar mass, we can calculate the number of moles using the mass of ethanol provided. For example, with 0.82 g of ethanol: \[ n = \frac{0.82 \text{ g}}{46.08 \text{ g/mol}} = 0.0178 \text{ moles} \] Converting the volume from milliliters to liters, 10.5 mL becomes 0.0105 L. Finally, applying the molarity formula: \[ M = \frac{0.0178 \text{ moles}}{0.0105 \text{ L}} = 1.70 \text{ M} \]

Ammonia and Molarity

Ammonia, represented as \( \text{NH}_3 \), is another common compound often used in chemistry. To calculate the molarity of an ammonia solution, we start by finding its molar mass: \[ 1 \text{ Nitrogen} \times 14.01 + 3 \text{ Hydrogens} \times 1.01 = 17.04 \text{ g/mol} \] Using this, we calculate the number of moles from the given mass of ammonia. For instance, with 1.27 g of ammonia: \[ n = \frac{1.27 \text{ g}}{17.04 \text{ g/mol}} = 0.0745 \text{ moles} \] Converting the solution volume from milliliters to liters, 33.5 mL becomes 0.0335 L. Using the molarity formula: \[ M = \frac{0.0745 \text{ moles}}{0.0335 \text{ L}} = 2.22 \text{ M} \]

What is Concentration in Chemistry?

Concentration measures how much of a solute is dissolved in a given quantity of solvent or solution. It can be expressed in various ways, but molarity is one of the most common units. Concentration helps chemists understand the strength and reactivity of solutions. When we say a solution has a high concentration, it means there are more solute particles in a given volume of the solution. Conversely, a low concentration means fewer solute particles. Concentration is crucial in reactions because the rate of reaction often depends on how many reactant particles are available to collide and react.

Basics of Solution Chemistry

Solution chemistry is a branch of chemistry dealing with solutions, or homogeneous mixtures of substances. Key terms include:

• Solute: The substance dissolved in the solution.
• Solvent: The substance in which the solute dissolves; often water.
• Solution: The uniform mixture of solute and solvent.

In solution chemistry, understanding how substances dissolve and interact is essential. For instance, when calculating the molarity of ethanol or ammonia, we are applying principles of solution chemistry. By knowing the solute's molar mass and the volume of the solution, we can determine the solution's concentration.