Question

A 1000.-mL solution of hydrochloric acid has a pH of 1.3. Calculate the mass (g) of HCl dissolved in the solution.

Short answer

The mass of HCl in the solution is approximately 1.83 grams.

Step-by-step solution

Understanding pH and Concentration

The pH of a solution is a measure of the concentration of hydrogen ions. The formula to convert pH to hydrogen ion concentration is: \[ [H^+] = 10^{-pH} \]For a pH of 1.3, we calculate the hydrogen ion concentration \([H^+]\): \[ [H^+] = 10^{-1.3} \approx 5.01 \times 10^{-2} \, M \]

Stoichiometry of HCl Dissociation

Hydrochloric acid, HCl, dissociates completely in water to form \(H^+\) and \(Cl^-\). Therefore, the concentration of HCl is equal to the concentration of \([H^+]\), which is \(5.01 \times 10^{-2} \, M\).

Calculate Moles of HCl

To find the total moles of HCl in the 1000 mL (or 1 L) of solution, use the formula: \[ ext{Moles of HCl} = ext{Concentration (M)} \times ext{Volume (L)} \] Therefore: \( ext{Moles of HCl} = 5.01 \times 10^{-2} \, M \times 1 \, L = 5.01 \times 10^{-2} \, ext{moles} \)

Calculate Mass of HCl

The mass of HCl can be calculated using its molar mass (36.46 g/mol). Multiply the number of moles by the molar mass: \[ ext{Mass of HCl} = ext{Moles} \times ext{Molar Mass} \] \( ext{Mass of HCl} = 5.01 \times 10^{-2} \, ext{moles} \times 36.46 \, ext{g/mol} \approx 1.83 \, g \)

Key concepts

pH concentration

The concept of pH is fundamental to understanding the acidic or basic nature of a solution. It quantifies the hydrogen ion concentration in a solution. The scale ranges from 0 to 14, where low values indicate high acidity and high values indicate alkalinity. The pH scale is logarithmic, meaning each whole number change on the scale represents a tenfold change in hydrogen ion concentration.

To calculate hydrogen ion concentration \([H^+]\) from pH, we use \( [H^+] = 10^{-\text{pH}} \).
For example, at pH 1.3, the calculation is \( 10^{-1.3} \), which results in a concentration of approximately \( 5.01 \times 10^{-2} \, M \).

Understanding pH helps determine how much of a substance, like HCl, has dissociated in a solution, which is key for further calculations.

stoichiometry

Stoichiometry involves understanding the relationships between reactants and products in a chemical reaction. In the case of hydrochloric acid (HCl) dissociating in water, the stoichiometric equation is:
\[ \text{HCl} \rightarrow \text{H}^+ + \text{Cl}^- \]

This equation shows that each molecule of HCl dissociates completely into one hydrogen ion \((H^+)\) and one chloride ion \((Cl^-)\).
Since the reaction goes to completion, the concentration of \([H^+]\) directly equals the initial concentration of HCl.

Stoichiometry within this context helps you relate the moles of HCl present to the moles of ions produced, providing a clear path from the concentration of ions to determining the original composition of the solution.

moles calculation

Calculating moles is crucial when transitioning from concentration to mass in chemical equations. The mole is a fundamental unit in chemistry that quantifies an amount of a substance. It allows chemists to express amounts in terms of measurable mass.

For a 1000 mL solution with a concentration of \(5.01 \times 10^{-2} \text{ M}\), moles are calculated as:
\[ \text{Moles of HCl} = \text{Concentration (M)} \times \text{Volume (L)} \]
Here, substituting the known values yields \(5.01 \times 10^{-2} \text{ moles}\).

By converting concentration and volume into moles, you bridge your way to calculating the total actual amount of a substance, moving closer to expressing it as mass.

molar mass

Molar mass is the mass of one mole of a substance, expressed in grams per mole (g/mol). It allows for converting between moles, a count of particles, and mass, a measurable quantity.

For hydrochloric acid (HCl), the molar mass is 36.46 g/mol. This value is derived from the combined atomic masses of hydrogen and chlorine as found on the periodic table.

To find the mass of HCl in the solution, the number of moles calculated is multiplied by the molar mass:
\[ \text{Mass of HCl} = \text{Moles} \times \text{Molar Mass} \]
Thus, with \(5.01 \times 10^{-2} \text{ moles}\) and the molar mass of 36.46 g/mol, you find the mass to be around \(1.83 \, g\).

Understanding molar mass is crucial for linking moles to a tangible mass, giving a complete picture of the quantity of a substance in a solution.