Lithium hydride reacts with water as follows.
LiH(s) + H2O(l) -->LiOH(aq) + H2(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 4.7 L life belt with hydrogen gas at 1.04 atm and 22.4°C?
how do i even start this problem?
Use PV = nRT to calculate moles H2 gas needed. Then put the H2 in the equation given and use stoichiometry to convert moles H2 to moles LiH, then to grams LiH
To solve this problem, you need to use the ideal gas law equation to calculate the number of moles of H2 gas produced, and then convert it to grams using the molar mass of LiH.
Here are the steps to solve the problem:
Step 1: Write down the given information:
- Volume of the life belt: 4.7 L
- Pressure of the hydrogen gas: 1.04 atm
- Temperature: 22.4°C
Step 2: Convert temperature to Kelvin:
The ideal gas law equation requires the temperature to be in Kelvin. Convert the given temperature from Celsius to Kelvin by adding 273.15 to it:
22.4°C + 273.15 = 295.55 K
Step 3: Use the ideal gas law equation to calculate the number of moles of H2:
The ideal gas law is defined as PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.
R = 0.0821 L·atm/(mol·K) (ideal gas constant)
To solve for n, rearrange the equation as follows:
n = PV / RT
Step 4: Calculate the number of moles of H2:
Substitute the given values into the equation:
n = (1.04 atm) * (4.7 L) / (0.0821 L·atm/(mol·K) * 295.55 K)
Step 5: Calculate the mass of LiH:
The balanced chemical equation shows that 1 mole of LiH produces 1 mole of H2. You can use this ratio to calculate the number of moles of LiH required. Then, multiply the number of moles by the molar mass of LiH to get the mass in grams.
The molar mass of LiH is:
Li: 6.94 g/mol
H: 1.01 g/mol
So, the molar mass of LiH is 6.94 g/mol + 1.01 g/mol = 7.95 g/mol.
Multiply the number of moles of H2 gas calculated in Step 4 by the molar mass of LiH to get the mass in grams:
Mass = n * molar mass of LiH
Step 6: Calculate the mass of LiH:
Finally, substitute the value of n into the equation:
Mass = (n) * (7.95 g/mol)
Perform the calculation to find the mass of LiH needed to fill the 4.7 L life belt with hydrogen gas.
To start solving this problem, we need to follow a few key steps:
1. Determine the balanced chemical equation: The given equation is already balanced: LiH(s) + H2O(l) --> LiOH(aq) + H2(g). This equation tells us that for every one molecule of LiH that reacts, one molecule of H2 is produced.
2. Convert the given volume to moles: The ideal gas law equation is PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin. Since we are given the volume in liters and the pressure in atmospheres, we can use the equation n = PV / RT to convert the given volume to moles.
3. Use stoichiometry to convert moles of H2 to moles of LiH: From the balanced chemical equation, we know that the ratio of moles of H2 to moles of LiH is 1:1. So, the number of moles of LiH needed will be the same as the number of moles of H2.
4. Convert moles of LiH to grams: The molar mass of LiH can be calculated by summing the atomic masses of lithium (Li) and hydrogen (H). Using the molar mass, we can convert moles of LiH to grams.
5. Calculate the final answer: Multiply the grams of LiH needed by the molar mass to determine the amount of LiH required to fill the life belt with hydrogen gas.
Let's proceed with these steps!