Problem 33 - Chemistry Principles and Practice

Question

Write the equation for the reaction of \(\mathrm{NaH}\) and water. What mass of \(\mathrm{NaH}\) is needed to prepare \(1.00 \mathrm{~L}\) hydrogen gas at \(25^{\circ} \mathrm{C}\) and 1.00 atm pressure?

Step-by-Step Solution

Answer

0.97 g of NaH is required to produce 1.00 L of hydrogen gas at 25°C and 1 atm.

Step 1: Write the balanced chemical equation

Determine the balanced chemical equation for the reaction between sodium hydride \(\mathrm{NaH}\) and water. The balanced chemical reaction is: \[\mathrm{NaH} + \mathrm{H_2O} \rightarrow \mathrm{NaOH} + \mathrm{H_2}\] This equation shows that one mole of \(\mathrm{NaH}\) reacts with one mole of water to produce one mole of sodium hydroxide \(\mathrm{NaOH}\) and one mole of hydrogen gas \(\mathrm{H_2}\).

Step 2: Use the ideal gas law to find moles of hydrogen gas

Use the ideal gas law equation \(PV = nRT\) to determine the number of moles of hydrogen gas required. Given: - Pressure \(P = 1.00\, \text{atm}\) - Volume \(V = 1.00\, \text{L}\)- Ideal gas constant \(R = 0.0821\, \text{L atm mol}^{-1}\text{K}^{-1}\)- Temperature \(T = 25^{\circ}\mathrm{C} = 298\, \text{K}\)Rearrange to solve for \(n\): \[n = \frac{PV}{RT} = \frac{1.00\, \text{atm} \times 1.00\, \text{L}}{0.0821\, \text{L atm mol}^{-1}\text{K}^{-1} \times 298\, \text{K}}\]Calculate the moles \(n\):\[n \approx 0.0404 \text{ mol}\]

Step 3: Relate moles of sodium hydride to moles of hydrogen gas

From the balanced equation, we know that 1 mole of \(\mathrm{NaH}\) produces 1 mole of \(\mathrm{H_2}\). Therefore, the moles of sodium hydride needed is the same as the moles of hydrogen gas.Thus, moles of \(\mathrm{NaH}\) required \(= 0.0404\, \text{mol}\).

Step 4: Calculate the mass of sodium hydride needed

Calculate the mass of sodium hydride required using its molar mass. The molar mass of \(\mathrm{NaH}\) is the sum of the molar masses of sodium \(\mathrm{Na}\) and hydrogen \(\mathrm{H}\):\[\mathrm{NaH} = 22.99 + 1.01 = 24.00\, \text{g/mol}\]The mass of sodium hydride required is then calculated by:\[\text{Mass} = \text{moles} \times \text{molar mass} = 0.0404\, \text{mol} \times 24.00\, \text{g/mol}\]\[\text{Mass} \approx 0.97 \text{ g}\]

Key Concepts

Ideal Gas Law

The Ideal Gas Law is a fundamental principle in chemistry that relates the pressure, volume, temperature, and number of moles of an ideal gas. This equation is expressed as \( PV = nRT \), where:

• \( P \) represents the pressure of the gas in atmospheres (atm)
• \( V \) is the volume of the gas in liters (L)
• \( n \) is the number of moles (mol)
• \( R \) is the ideal gas constant, approximately 0.0821 L atm mol^-1K^-1
• \( T \) is the temperature in Kelvin (K)

This equation provides a useful way to determine unknown variables when the others are given. For example, when finding how much hydrogen gas is produced in a reaction, you can rearrange the equation to solve for \( n \): \[ n = \frac{PV}{RT} \] This helps calculate the moles of gas needed, as shown in the step-by-step solution for producing hydrogen gas from sodium hydride.

Balancing Chemical Equations

Balancing chemical equations is an essential skill in chemistry. It ensures that the number of atoms for each element is the same on both sides of the equation, reflecting the law of conservation of mass. This means matter is neither created nor destroyed in a chemical reaction.
In the reaction between sodium hydride (\( \text{NaH} \)) and water (\( \text{H}_2\text{O} \)), the balanced equation is: \[ \text{NaH} + \text{H}_2\text{O} \rightarrow \text{NaOH} + \text{H}_2 \] Here, you can see that for each reactant and product, there is an equal amount of sodium, hydrogen, and oxygen atoms.
Balancing equations is typically achieved by adjusting coefficients, the standard "lowercase numbers" that multiply the entire entity in the equation, without altering subscripts within formulas. This ensures that chemical identity doesn't change and only quantities are adjusted to balance.

Molar Mass Calculation

The molar mass is the mass of one mole of a substance, expressed in grams per mole. It is calculated by summing the atomic masses of all atoms in one mole of a compound.
In the exercise, calculating the molar mass of sodium hydride (\( \text{NaH} \)) involves adding up the atomic masses of sodium (Na) and hydrogen (H):

• Sodium (Na): Approximately 22.99 g/mol
• Hydrogen (H): Approximately 1.01 g/mol

Thus, the molar mass of \( \text{NaH} \) is: \[ \text{NaH} = 22.99 + 1.01 = 24.00\, \text{g/mol} \] Once you have the molar mass, you can determine how much of the compound you have in a given amount by multiplying the moles by the molar mass: \[ \text{Mass} = \text{moles} \times \text{molar mass} = 0.0404\, \text{mol} \times 24.00\, \text{g/mol} \] This calculation shows that roughly 0.97 grams of \( \text{NaH} \) is required to produce the desired amount of hydrogen gas.