Question

What volume of hydrogen chloride gas at STP is required to prepare \(500 . \mathrm{mL}\) of \(0.100 \mathrm{MHCl}\) solution?

Short answer

To prepare 500 mL of 0.100 M HCl solution, 1.1224 L of hydrogen chloride gas at STP is required.

Step-by-step solution

Find the number of moles of HCl needed for the solution

We know the volume and molarity of the solution, so we can use the formula: Moles of solute = Molarity × Volume of solution Substituting the values we have: Moles of HCl = \(0.100 \, mol/L\) × \(0.500 \, L\) Moles of HCl = \(0.050 \, mol\)

Use the ideal gas law to find the volume of HCl gas at STP

We will use the ideal gas law to find the volume of HCl gas at STP. The equation is: \(PV = nRT\) At standard temperature and pressure (STP), the conditions are: Pressure (P) = \(1 \, atm\) Temperature (T) = \(273.15 \, K\) Ideal gas constant (R) = \(0.0821 \frac{L \cdot atm}{mol \cdot K}\) We have already calculated the number of moles of HCl (n) in Step 1. Now we will solve for the volume (V). Rearranging the ideal gas law equation, we get: \(V = \frac{nRT}{P}\) Substituting the values: \(V = \frac{(0.050 \, mol) (0.0821 \frac{L \cdot atm}{mol \cdot K}) (273.15 \, K)}{1 \, atm}\) \(V = 1.1224 \, L\) Therefore, 1.1224 L of hydrogen chloride gas at STP is required to prepare 500 mL of 0.100 M HCl solution.

Key concepts

Molarity Calculation

Understanding molarity is crucial for various scientific calculations. In chemistry, molarity refers to the concentration of a solution, which is expressed as the number of moles of a solute per liter of solution. The unit for molarity is mol/L and is often designated with a capital M.

To calculate molarity, you can use this simple formula:
\[\text{Molarity} = \frac{\text{Moles of solute}}{\text{Volume of solution in liters}}\]
Considering the exercise mentioned, the goal is to prepare a 0.100 M solution of hydrogen chloride (HCl). The volume of this solution is given as 500 mL, which is equivalent to 0.500 liters. By using the molarity formula, it's determined that you need 0.050 moles of HCl for this specific volume of solution.

It's important for students to remember to convert the volume from milliliters to liters when using such formulas because molarity is defined per liter of solution. This is a common area where errors can occur during molarity calculations. Also, precise measurements are critical to achieving the correct molarity of a resulting solution.

Stoichiometry

Stoichiometry is at the heart of chemical reactions. It's a section of chemistry that involves quantitatively analyzing the relationships between reactants and products in a chemical reaction. Stoichiometry hinges on the conservation of mass and the principles of the balanced chemical equation. It uses the mole concept as a bridge between the microscopic world of atoms and molecules and the macroscopic world we observe.

When applying stoichiometry to solve problems, one typically follows these steps:

• Write the balanced equation for the reaction.
• Convert the quantities of known substances into moles.
• Use the coefficients from the balanced equation to calculate the moles of the desired product or reactant.
• Convert the moles back into the desired units (grams, liters, molecules, etc.).

In the context of the exercise provided, stoichiometry is applied to relate the moles of HCl gas required to the volume of the gas at STP (standard temperature and pressure). The mole is a key unit in stoichiometry as it allows for this connection between the amount of substance and the volume of gas.

Ideal Gas Law

The ideal gas law is a fundamental equation that describes the state of an ideal gas. It is often represented as PV=nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is temperature.

The ideal gas law allows us to predict the behavior of gases under various conditions of pressure, volume, temperature, and amount. In the context of preparing hydrogen chloride gas, we use the ideal gas law to calculate the volume of HCl gas required to prepare a given molarity of solution at STP conditions.

To solve for volume at STP (1 atm pressure and 273.15 K temperature) using the values from the exercise:
\[V = \frac{nRT}{P}\]Given that R (the gas constant) is \(0.0821 \frac{L \cdot atm}{mol \cdot K}\), n is the number of moles of HCl (0.050 mol), and both P and T are known for STP, direct substitution yields the volume of HCl gas needed. For students to fully grasp this ideal gas law calculation, it's crucial to understand each variable and how they interrelate. This understanding allows them to manipulate the formula for different conditions beyond STP or calculate other variables when given sufficient information.