Consider the combustion reaction between 1.00 L of liquid methanol (density = 0.850 g/mL) and 500 L of oxygen gas measured at STP. The products of the reaction are CO2(g) and H2O(g). Calculate the volume of liquid H2O formed if the reaction goes to completion and you condense the water vapor.

Verified step by step guidance

Step 1: Write the balanced chemical equation for the combustion of methanol (CH3OH). The reaction is: \[ 2 \text{CH}_3\text{OH} (l) + 3 \text{O}_2 (g) \rightarrow 2 \text{CO}_2 (g) + 4 \text{H}_2\text{O} (g) \].

Step 2: Calculate the mass of methanol using its volume and density. Use the formula: \[ \text{mass} = \text{density} \times \text{volume} \]. Convert the volume from liters to milliliters first.

Step 3: Convert the mass of methanol to moles using its molar mass. The molar mass of methanol (CH3OH) is approximately 32.04 g/mol. Use the formula: \[ \text{moles} = \frac{\text{mass}}{\text{molar mass}} \].

Step 4: Determine the limiting reactant by comparing the mole ratio of methanol to oxygen gas. At STP, 1 mole of gas occupies 22.4 L. Calculate the moles of oxygen gas using its volume and compare it to the stoichiometric ratio from the balanced equation.

Step 5: Calculate the moles of water produced using the stoichiometry of the balanced equation. Then, convert the moles of water to volume using the density of water (1 g/mL) and the molar mass of water (18.02 g/mol). Use the formula: \[ \text{volume} = \frac{\text{moles} \times \text{molar mass}}{\text{density}} \].

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Stoichiometry

Stoichiometry is the branch of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. It allows us to calculate the amounts of substances consumed and produced in a reaction based on balanced chemical equations. In this case, understanding the stoichiometric ratios of methanol and oxygen in the combustion reaction is essential for determining the volume of water produced.

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. At standard temperature and pressure (STP), one mole of an ideal gas occupies 22.4 L. This concept is crucial for converting the volume of oxygen gas into moles, which can then be used in stoichiometric calculations to find the amount of water produced in the reaction.

Density and Volume Conversion

Density is defined as mass per unit volume and is a key concept for converting between the mass of a substance and its volume. In this problem, the density of liquid methanol is used to convert its volume (1.00 L) into mass, which is necessary for determining how much methanol reacts with oxygen. Additionally, understanding how to convert the mass of water produced back into volume after condensation is essential for the final calculation.

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