One of the causes of the explosion at Chernobyl may have been the reaction between zirconium, which coated the fuel rods, and steam. $$\mathrm{Zr}(s)+2 \mathrm{H}_{2} \mathrm{O}(g) \longrightarrow \mathrm{ZrO}_{2}(s)+2 \mathrm{H}_{2}(g)$$ If half a metric ton of zirconium reacted, what pressure was exerted by the hydrogen gas produced at \(55^{\circ} \mathrm{C}\) in the containment chamber, which had a volume of \(2.0 \times 10^{4} \mathrm{~L} ?\)

Stoichiometry is a section of chemistry that focuses on the quantitative relationships between the reactants and products in a chemical reaction. By using the coefficients from the balanced chemical equation, you can determine how much of one substance will react with, or be produced from, a certain amount of another substance.

For instance, in the reaction at Chernobyl involving zirconium and steam, the equation tells us that one mole of Zirconium (Zr) reacts with two moles of water (H₂O) to produce one mole of Zirconium dioxide (ZrO₂) and two moles of hydrogen gas (H₂). This stoichiometric ratio of 1:2:1:2 is essential to calculate the amount of hydrogen gas produced when you know the amount of zirconium that reacted.

To improve understanding, visualize stoichiometry as a recipe – if you know how much of one ingredient you have, you can calculate how much of the others you need to complete the recipe.

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). It can be calculated by summing the atomic masses of the elements in a compound as listed on the periodic table. The molar mass serves as a conversion factor that allows us to convert between the mass of a substance and the number of moles in that substance.

For the calculation tied to the Chernobyl incident, understanding molar mass is crucial. Given that the molar mass of Zirconium is 91.22 g/mol, you can determine how many moles are in half a metric ton of Zirconium by dividing the total mass in grams by the molar mass. This step is essential because stoichiometry calculations require amounts in moles, not grams, in order to use the balanced chemical equation effectively.

Think of molar mass as the 'price per mole' — just as you'd calculate the cost for a number of items given the price per item, here, you calculate the number of moles given the 'price' (molar mass) per mole.

Gas pressure calculations often involve understanding how the measurable properties of a gas—like pressure, volume, temperature, and number of moles—relate to each other. For gases, this relationship is described by the Ideal Gas Law, which is expressed as PV=nRT. This formula allows you to solve for any one of the variables if the others are known.

In the Chernobyl example, the task is to find the pressure exerted by hydrogen gas. Once we've used stoichiometry to find the moles of hydrogen and figured out the molar mass of Zirconium, we know the 'n' in the Ideal Gas Law. By inputting this value, along with the volume of the containment chamber ('V'), the temperature in Kelvin ('T'), and the universal gas constant ('R'), you can solve for pressure ('P').

It's crucial to ensure that the units are consistent when applying the Ideal Gas Law. For example, temperature must be in Kelvin, and volume should match the units of the gas constant (liters in this case). Consider the gas constant 'R' as a standardized 'gas currency exchange rate,' translating moles, temperature, and volume into pressure.