A railroad tank car derails and spills 36 tons of concentrated sulfuric acid. The acid is 98.0 mass% H2SO4 and has a density of 1.836 g/mL. (c) How many liters of carbon dioxide at 18 °C and 745 mm Hg are produced as a by-product?

Verified step by step guidance

First, calculate the mass of pure H2SO4 in the spilled sulfuric acid. Since the acid is 98.0 mass% H2SO4, multiply the total mass of the acid (36 tons) by 0.98 to find the mass of H2SO4.

Convert the mass of H2SO4 from tons to grams. Use the conversion factor: 1 ton = 1,000,000 grams.

Determine the volume of the sulfuric acid solution using its density. Use the formula: \( \text{Volume} = \frac{\text{Mass}}{\text{Density}} \). Convert the mass of the solution from grams to milliliters using the density of 1.836 g/mL.

Use the stoichiometry of the chemical reaction between sulfuric acid and a carbonate (e.g., calcium carbonate) to find the moles of CO2 produced. The balanced equation is: \( \text{H}_2\text{SO}_4 + \text{CaCO}_3 \rightarrow \text{CaSO}_4 + \text{CO}_2 + \text{H}_2\text{O} \). Calculate the moles of CO2 based on the moles of H2SO4.

Convert the moles of CO2 to liters using the ideal gas law \( PV = nRT \). Use the given conditions: temperature (18 °C, converted to Kelvin) and pressure (745 mm Hg, converted to atm). Solve for the volume \( V \) in liters.

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. Understanding stoichiometry is essential for determining how much carbon dioxide is produced from the sulfuric acid in this scenario.

Ideal Gas Law

The Ideal Gas Law is a fundamental equation in chemistry that relates the pressure, volume, temperature, and number of moles of a gas. It is expressed 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 in Kelvin. This law is crucial for calculating the volume of carbon dioxide produced under specific conditions of temperature and pressure.

Concentration and Density

Concentration refers to the amount of a substance in a given volume of solution, often expressed in mass percent or molarity. Density, on the other hand, is the mass of a substance per unit volume, typically expressed in grams per milliliter. In this problem, understanding the mass percent of sulfuric acid and its density is necessary to convert the mass of the acid into volume, which is a key step in determining the amount of carbon dioxide produced.

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