A railroad tank car derails and spills 36 tons of...

A railroad tank car derails and spills 36 tons of concentrated sulfuric acid. The acid is 98.0 mass $\% {H}_{2} {SO}_{4}$ and has a density of 1.836 ${g} / {mL.}$ (a) What is the molarity of the acid? (b) How many kilograms of sodium carbonate are needed to completely neutralize the acid? (c) How many liters of carbon dioxide at 18 °C and 745 mm Hg are produced as a byproduct?

A railroad tank car derails and spills 36 tons of concentrated sulfuric acid. The acid is 98.0 mass $\% {H}_{2} {SO}_{4}$ and has a density of 1.836 ${g} / {mL.}$
(a) What is the molarity of the acid?
(b) How many kilograms of sodium carbonate are needed to completely neutralize the acid?
(c) How many liters of carbon dioxide at 18 °C and 745 mm Hg are produced as a byproduct?

Key Concepts

Ideal Gas Law

The Ideal Gas Law, expressed as PV = nRT, relates the pressure, volume, temperature, and number of moles of a gas. This concept is applied to calculate the volume occupied by a gas under certain conditions of temperature and pressure, which is particularly useful when dealing with gaseous byproducts in chemical reactions.

Neutralization Reactions

Neutralization reactions occur when an acid reacts with a base to produce water and a salt. In such reactions, the moles of acid and base react in proportion to the balanced chemical equation. Understanding this concept enables the computation of the exact amount of a base required to neutralize an acid, which is important in many practical applications such as titrations and industrial processes.

Stoichiometry and Balanced Chemical Equations

Stoichiometry involves using balanced chemical equations to relate the quantities of reactants and products in a chemical reaction. This concept is key to calculating how much of one substance is needed to react completely with another, as well as in predicting the amounts of products formed. The stoichiometric coefficients from the balanced equation provide the mole ratio between reactants and products.

Mass Percent Composition

Mass percent composition indicates the ratio of the mass of a specific component to the total mass of the solution, expressed as a percentage. This concept is crucial for determining the actual mass of the active component in a mixture or solution, and it serves as a starting point for further calculations such as converting to moles or determining concentrations.

Molarity

Molarity is a measure of concentration that expresses the number of moles of a solute per liter of solution. It is calculated by dividing the moles of the solute, which can be derived from the mass and molar mass, by the total volume of the solution in liters. This concept is fundamental in solution chemistry and is frequently used to describe the concentration of acids, bases, and other dissolved substances.

Density and Volume Conversions

Density is defined as mass per unit volume and is used to convert between these two quantities. In practice, knowing the density of a solution allows one to determine its volume from a given mass, or vice versa, which is essential for preparing solutions and performing concentration calculations.

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