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 \(\mathrm{LiH}\) would react with the seawater and fill their life jackets and lifeboats with hydrogen gas. How many grams of \(\mathrm{LiH}\) are needed to fill a 4.1-L life jacket at 0.97 atm and \(12^{\circ} \mathrm{C}\) ?

Short answer

1.376 grams of LiH are needed.

Step-by-step solution

Understand the Reaction

The chemical equation given is \( \mathrm{LiH}(s) + \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{LiOH}(aq) + \mathrm{H}_{2}(g) \). This means that lithium hydride reacts with water to produce lithium hydroxide and hydrogen gas.

Calculate Moles of Hydrogen Gas

Use the ideal gas law equation \( PV = nRT \) to calculate the moles of hydrogen gas \( n \). First, convert the temperature from Celsius to Kelvin: \( T = 12^{\circ}\mathrm{C} + 273.15 = 285.15 \, K \). The given pressure \( P = 0.97 \, atm \), volume \( V = 4.1 \, L \), and the ideal gas constant \( R = 0.0821 \, \text{L atm K}^{-1}\, \text{mol}^{-1} \). Substitute these values into the equation: \( n = \frac{PV}{RT} = \frac{(0.97 \, atm)(4.1 \, L)}{(0.0821 \text{ L atm K}^{-1} \text{mol}^{-1})(285.15 \, K)} \approx 0.173 \, mol \).

Relate Moles of Hydrogen to Moles of LiH

According to the balanced chemical equation, 1 mole of \( \mathrm{LiH} \) produces 1 mole of \( \mathrm{H}_{2} \). Thus, 0.173 moles of \( \mathrm{H}_{2} \) means 0.173 moles of \( \mathrm{LiH} \) are required.

Calculate Mass of LiH Required

The molar mass of \( \mathrm{LiH} \) is approximately 7.95 g/mol (Lithium: 6.94 g/mol + Hydrogen: 1.01 g/mol). Therefore, the mass of \( \mathrm{LiH} \) needed is \( 0.173 \, mol \times 7.95 \, g/mol \approx 1.376 \, g \).

Key concepts

Ideal Gas Law

The Ideal Gas Law is a fundamental principle in chemistry that relates the properties of an ideal gas. Commonly expressed as \( PV = nRT \), this equation connects pressure (\( P \)), volume (\( V \)), temperature (\( T \)), and the amount of gas in moles (\( n \)). The constant \( R \) is the ideal gas constant, valued at 0.0821 L atm K^{-1} mol^{-1}.
By rearranging the equation, you can solve for any variable, given the other three are known. This makes the Ideal Gas Law incredibly useful in a wide array of problems, such as determining the amount of gas required in a specific reaction or understanding how gas behavior changes under different conditions.
For students, mastering the Ideal Gas Law allows for better comprehension of gas behaviors in both controlled laboratory settings and real-world scenarios.

Chemical Reactions

Chemical reactions are processes where substances transform into new substances. The given reaction of lithium hydride with water is a great example: \( \mathrm{LiH}(s) + \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{LiOH}(aq) + \mathrm{H}_{2}(g) \).
This reaction releases hydrogen gas, which was used historically to fill life jackets for flotation. Each component of the reaction serves a specific role:

• Lithium hydride (\( \mathrm{LiH} \)) reacts with water.
• Water (\( \mathrm{H}_{2} \mathrm{O} \)) acts as a reactant, facilitating the production of new substances.
• The products are lithium hydroxide (\( \mathrm{LiOH} \)), which remains dissolved in water, and hydrogen gas (\( \mathrm{H}_{2} \)), which can be captured or used.

Understanding these reactions helps predict the outcomes, establish equations, and calculate amounts needed for practical applications.

Molar Mass Calculation

Molar mass is the mass of one mole of a substance, essential for converting between grams and moles. Calculating molar mass involves summing the atomic masses of each element in a compound, found on the periodic table.
In the problem, the molar mass of lithium hydride (\( \mathrm{LiH} \)) is calculated as:

• Lithium (\( \mathrm{Li} \)): 6.94 g/mol
• Hydrogen (\( \mathrm{H} \)): 1.01 g/mol

Combining these values gives \( 7.95 \) g/mol for \( \mathrm{LiH} \). This calculation allows the conversion of moles to grams, vital for quantifying how much \( \mathrm{LiH} \) is necessary for the reaction, as demonstrated in the exercise.
Understanding molar mass also supports efficient resource planning in chemical processes.

Lithium Hydride Reaction

The reaction between lithium hydride and water is noteworthy both for its historical use and simplicity. When \( \mathrm{LiH} \) contacts water, it reacts quickly and efficiently to produce hydrogen gas and lithium hydroxide:
\( \mathrm{LiH}(s) + \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{LiOH}(aq) + \mathrm{H}_{2}(g) \).
This reaction was crucial during World War II, providing an emergency source of hydrogen gas. The properties of \( \mathrm{LiH} \) make it an excellent candidate for such applications due to its ability to rapidly release hydrogen, aiding in the flotation of life-saving equipment.
The straightforward 1:1 mole ratio simplifies calculations and ensures predictability in how much reactant is needed. It's a prime example of applying chemistry to solve real-world problems efficiently.