Question

Lithium hydride reacts with water as follows: $$\mathrm{LiH}(s)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{LiOH}(a q)+\mathrm{H}_{2}(g)$$ During World War II, U.S. pilots carried LiH tablets. In the event of a crash landing at sea, the LiH would react with the seawater and fill their life belts and lifeboats with hydrogen gas. How many grams of LiH are needed to fill a \(4,1-\mathrm{L}\) life belt at \(0.97 \mathrm{~atm}\) and \(12^{\circ} \mathrm{C} ?\)

Short answer

The mass of LiH required in grams can be calculated using the steps explained above.

Step-by-step solution

Calculate the number of moles of hydrogen gas

Using the ideal gas law, \(PV=nRT\), it's possible to solve for 'n', which is the number of moles of gas. Here, P = 0.97 atm, V = 4.1 L (converted from mL to L), R is the gas constant = 0.0821 L. atm/K. mol, and T is the absolute temperature in Kelvin (12 + 273.15 = 285.15 K). So, \(n = \frac{PV}{RT} = \frac{0.97 \times 4.1}{0.0821 \times 285.15}\)

Use Stoichiometry to Calculate Moles of LiH

In this reaction, each mole of LiH produces one mole of \(H_{2}\) gas. Therefore, the number of moles of \(H_{2}\) gas previously calculated is equal to the necessary number of moles of LiH.

Calculate the Mass of LiH in grams

Next, convert the moles of LiH to grams using its molar mass. The molar mass of LiH is 7.94 g/mol. Multiply the number of moles of LiH by its molar mass to get the mass in grams.

Key concepts

Lithium Hydride

Lithium hydride, abbreviated as LiH, is a compound where lithium, a light and highly reactive metal, combines with hydrogen to form a solid, ionic hydride. In chemical reactions, LiH serves as a strong reducing agent. When it is added to water, it reacts vigorously to produce lithium hydroxide (LiOH) and hydrogen gas (H₂).

• The reaction between LiH and water can be shown as: \[\mathrm{LiH}(s) + \mathrm{H}_{2}\mathrm{O}(l) \rightarrow \mathrm{LiOH}(aq) + \mathrm{H}_{2}(g)\]
• The evolved hydrogen gas is what makes LiH particularly useful in emergency situations, such as during World War II, where it could fill life belts with buoyant hydrogen gas.

This highly energetic reaction makes LiH both a useful and a hazardous material to handle. Safety while storing and using LiH is crucial due to its reactivity, especially in the presence of water.

Stoichiometry

Stoichiometry involves the calculation of reactants and products in chemical reactions. It's a fundamental concept in chemistry that helps in predicting yields in reactions.
In the case of the reaction between lithium hydride (LiH) and water, stoichiometry can be used to determine how much LiH is needed to generate a certain amount of hydrogen gas.

• This process involves using the balanced chemical reaction and the principles of mole ratios. In the reaction: \[\mathrm{LiH}(s) + \mathrm{H}_{2}\mathrm{O}(l) \rightarrow \mathrm{LiOH}(aq) + \mathrm{H}_{2}(g)\]1 mole of LiH is required to produce 1 mole of hydrogen gas.
• Once the number of moles of hydrogen is calculated using the Ideal Gas Law, it becomes straightforward to determine the moles of LiH needed, as they are in a 1:1 ratio.

Understanding stoichiometry is essential not only for predicting the outcome of chemical reactions but also for scaling reactions up or down in laboratory or industrial settings.

Molar Mass Calculations

Molar mass is a crucial concept when converting the amount of a substance in moles to a measurable mass in grams, especially when dealing with chemical reactions.
For lithium hydride (LiH), its molar mass can be calculated by adding the atomic mass of lithium (approximately 6.94 g/mol) and hydrogen (approximately 1.01 g/mol).

• Thus, the molar mass of LiH equals 7.94 g/mol. This figure is used to convert moles of LiH, computed through stoichiometric calculations, into grams.
• For example, if 0.12 moles of LiH are needed, the total mass is calculated by multiplying 0.12 moles by 7.94 g/mol, resulting in approximately 0.9528 grams of LiH.

Molar mass calculations form the bridge between measuring substances in the laboratory and applying theoretical chemistry concepts practically. It allows chemists to precisely measure reagents and predict reaction yields.