Problem 108 - Chemistry

Question

The volume of a sample of pure HCl gas was \(189 \mathrm{~mL}\) at \(25^{\circ} \mathrm{C}\) and \(108 \mathrm{mmHg} .\) It was completely dissolved in about \(60 \mathrm{~mL}\) of water and titrated with an \(\mathrm{NaOH}\) solution; \(15.7 \mathrm{~mL}\) of the \(\mathrm{NaOH}\) solution were required to neutralize the \(\mathrm{HCl}\). Calculate the molarity of the \(\mathrm{NaOH}\) solution.

Step-by-Step Solution

Answer

The molarity of the NaOH solution is \(0.57 \text{ M}\).

Step 1: Calculate the moles of HCl gas

The moles of a gas can be calculated using the Ideal Gas Law, \(PV = nRT\), where P represents pressure, V volume, n the number of moles, R the ideal gas constant, and T the temperature in Kelvin. Converting given temperature to Kelvin (25°C + 273 = 298 K) and pressure to atm (108 mmHg / 760 mmHg = 0.142 atm), we solve the equation for n: \[n = \frac{PV}{RT} = \frac{0.142 \times 0.189}{0.0821 \times 298} = 0.00896 \text{ moles}\]

Step 2: Find the neutralization reaction

HCl reacts with NaOH to form water and NaCl in a 1:1 ratio: \(HCl + NaOH \rightarrow H_2O + NaCl\). The number of moles of NaOH needed to neutralize HCl equals the number of moles of HCl. Therefore, 0.00896 moles of NaOH were used.

Step 3: Calculate the molarity of NaOH solution

Molarity (M) is defined as the number of moles of solute per liter of solution. Converting the volume of NaOH solution used to liters (15.7 mL = 0.0157 L), the molarity can be computed as: \[M = \frac{n}{V} = \frac{0.00896}{0.0157} = 0.57 \text{ M}\]

Key Concepts

Ideal Gas Law

The Ideal Gas Law is a fundamental equation in chemistry and physics, represented by the formula \( PV = nRT \). This equation relates the pressure \( P \), volume \( V \), and temperature \( T \) of a given amount of gas (in moles, \( n \)) with the universal gas constant \( R \). To solve for unknown quantities like moles of gas, as in this exercise, you need to rearrange the equation:

• Convert temperature from Celsius to Kelvin using the formula: \( T(K) = T(°C) + 273 \).
• Convert pressure to atmospheres if given in mmHg, using: \( 1 \, \mathrm{atm} = 760 \, \mathrm{mmHg} \).
• Insert these values into the rearranged equation \( n = \frac{PV}{RT} \) to find the moles of gas.

Regarding the given problem, converting the volume of the gas to liters is also essential (189 mL = 0.189 L). By inserting the converted values into the Ideal Gas Law, we can solve for the moles of HCl in the given conditions. Expanded knowledge on the Ideal Gas Law can greatly enhance predictions about gas behavior under different conditions.

HCl Neutralization

Neutralization is a chemical reaction in which an acid and a base react to form water and a salt. Here, hydrochloric acid (HCl) serves as the acid, and its neutralization occurs when it reacts with a base like sodium hydroxide (NaOH).

• This process is represented by the simple equation: \( \mathrm{HCl} + \mathrm{NaOH} \rightarrow \mathrm{H_2O} + \mathrm{NaCl} \).
• The reaction follows a stoichiometric 1:1 molar ratio, meaning one mole of HCl will require precisely one mole of NaOH to be completely neutralized.
• This concept applies directly to the exercise because the number of moles of NaOH needed equals the moles of HCl initially calculated.

Understanding neutralization helps in various practical applications such as titrations, where determining the concentration of a solution by reacting it with a standard solution is crucial.

NaOH Titration

Titration is a common laboratory technique used to determine the concentration of an unknown solution. In this exercise, we use the NaOH solution as the titrant to find its molarity through the reaction with a known amount of HCl.

• You titrate until the reaction reaches the equivalence point, where equal moles of acid and base have reacted.
• Using a burette, you measure the volume of NaOH solution required to reach this point as precisely as possible. In this case, 15.7 mL of NaOH was used.
• The molarity of the NaOH solution is then calculated by dividing the moles of NaOH (determined from the equivalence point) by the volume in liters (15.7 mL = 0.0157 L).

Performing titrations accurately depends on attention to detail, including careful measurement and controlling for factors like the presence of indicators, which show when neutralization occurs.

Chemical Stoichiometry

Chemical stoichiometry involves calculating the relationships between reactants and products in chemical reactions. It is indispensable for ensuring that reactions are balanced appropriately.

• In stoichiometry, coefficients in balanced chemical equations indicate the ratio of moles of each substance involved. For the reaction \( \mathrm{HCl} + \mathrm{NaOH} \rightarrow \mathrm{H_2O} + \mathrm{NaCl} \), the stoichiometry is simply 1:1.
• Using stoichiometry, you can determine how much reactant is needed or how much product will be formed. In this problem, it helps confirm the amount of NaOH needed to neutralize a given amount of HCl.
• Stoichiometric calculations also extend to converting between units, such as from moles to grams or liters, lining this field of work closely with the Ideal Gas Law and titrations.

Developing proficiency in stoichiometry is crucial for any chemist, as it plays a key role in both laboratory settings and industrial applications.