Question

A chemist decides to prepare some chlorine gas by the following reaction: \(\mathrm{MnO}_{2}+4 \mathrm{HCl} \rightarrow \mathrm{MnCl}_{2}+2 \mathrm{H}_{2} \mathrm{O}+\mathrm{Cl}_{2} \uparrow\) If he uses \(100 \mathrm{~g}\) of \(\mathrm{MnO}_{2}\), what is the maximum volume of chlorine gas that can be obtained at standard temperature and pressure (STP)?

Short answer

The maximum volume of chlorine gas that can be obtained at STP is approximately \(25.76 L\).

Step-by-step solution

Calculate the moles of MnO₂

First, we need to determine the number of moles of MnO₂ used in the reaction. To do this, we can use the molar mass of MnO₂: Molar mass of MnO₂ = Molar mass of Mn + 2 * Molar mass of O Molar mass of MnO₂ = 54.94 g/mol (from periodic table) + 2 * 16.00 g/mol (from periodic table) Molar mass of MnO₂ = 86.94 g/mol Now, we can use the mass of MnO₂ (100 g) and its molar mass to calculate the number of moles: moles of MnO₂ = mass of MnO₂ / molar mass of MnO₂ moles of MnO₂ = 100 g / 86.94 g/mol moles of MnO₂ ≈ 1.15 mol

Determine the moles of Cl₂ produced

According to the balanced chemical equation, 1 mole of MnO₂ reacts with 4 moles of HCl to produce 1 mole of Cl₂: MnO₂ + 4 HCl → MnCl₂ + 2 H₂O + Cl₂ As we have calculated the moles of MnO₂ to be approximately 1.15 mol, we can determine the number of moles of Cl₂ produced by the reaction: moles of Cl₂ = moles of MnO₂ moles of Cl₂ ≈ 1.15 mol

Convert moles of Cl₂ to volume at STP

Now we can use the molar volume of an ideal gas at STP (1 mole of an ideal gas occupies 22.4 L at STP) to calculate the volume of Cl₂: volume of Cl₂ = moles of Cl₂ * molar volume at STP volume of Cl₂ = 1.15 mol * 22.4 L/mol volume of Cl₂ ≈ 25.76 L The maximum volume of chlorine gas that can be obtained at STP is approximately 25.76 L.

Key concepts

molar volume

Molar volume is a key concept in chemistry that refers to the volume occupied by one mole of a substance, usually a gas, under specified conditions. At Standard Temperature and Pressure (STP), which is defined as 0 degrees Celsius and 1 atm pressure, the molar volume of an ideal gas is 22.4 liters. This means that one mole of any gas at STP will occupy a volume of 22.4 liters. It's important to note that this relationship holds true under the assumption that the gas behaves ideally, meaning it follows the ideal gas law where the volume of the gas is directly proportional to the number of moles when the temperature and pressure are constant. This simplification makes it easier to predict and calculate how gases will behave in reactions and under different conditions. For the chemist in the exercise, knowing the molar volume allows them to convert from moles of chlorine gas calculated to the volume that it would occupy at STP, ensuring accurate predictions of the gas's behavior in practical applications.

molar mass

Molar mass is a crucial concept in stoichiometry, as it links mass and moles. It is defined as the mass of one mole of a substance and is usually expressed in grams per mole (g/mol). The molar mass of a compound can be calculated by summing the molar masses of its constituent elements, which can be found on the periodic table. For example, in the given exercise, the molar mass of MnO₂ is calculated as follows:

• Molar mass of Mn = 54.94 g/mol
• Molar mass of O = 16.00 g/mol
• Total molar mass of MnO₂ = 54.94 g/mol + 2 * 16.00 g/mol = 86.94 g/mol

Calculating the molar mass is a fundamental step in determining how much of a substance is present in moles, which can then be used to predict other variables like gaseous volumes.

balanced chemical equation

A balanced chemical equation is essential in stoichiometry because it accurately represents the conservation of mass and atoms in a chemical reaction. Balancing equations requires that the number of atoms for each element is the same on both the reactant and product sides of the equation. This is derived from the law of conservation of mass, which states that mass is neither created nor destroyed in a chemical reaction. In the given exercise, the balanced equation is:\[\mathrm{MnO}_{2} + 4\mathrm{HCl} \rightarrow \mathrm{MnCl}_{2} + 2\mathrm{H}_{2} \mathrm{O} + \mathrm{Cl}_{2}\]This equation shows that one mole of MnO₂ reacts with four moles of HCl to produce one mole of MnCl₂, two moles of H₂O, and one mole of Cl₂. The stoichiometric coefficients (the numerical coefficients before substances) are critical as they determine the ratio in which reactants combine and products form. This understanding allows chemists to use these coefficients to calculate moles and subsequently volumes or masses of reactants and products.

moles calculation

Moles calculation is a fundamental aspect of stoichiometry that involves converting between mass and moles using the molar mass of a substance. The relationship is given by the formula \[moles = \frac{\text{mass}}{\text{molar mass}}\]This calculation allows chemists to take a given mass of a substance, such as the 100 g of MnO₂ in the exercise, and determine how many moles that mass represents. Using the molar mass of MnO₂, which is 86.94 g/mol, the moles of MnO₂ can be calculated as:\[\text{moles of MnO}_2 = \frac{100\, \text{g}}{86.94\, \text{g/mol}} \approx 1.15\, \text{mol}\]Determining the number of moles is crucial as it serves as the basis for further calculations, such as using the balanced chemical equation to find out the moles of other substances produced or consumed in the reaction. The conversion from moles to volume, especially when dealing with gases, relies on this initial step to ensure accurate and meaningful results.