What mass of lithium (in g) is required to react completely with 57.5mL of N2 gas at STP? Lithium reacts with nitrogen gas according to the following reaction:
6Li(s)+N2(g)→2Li3N(s)
mols N2 = 57.5/22,400 = ?
mols Li = 6x that (from the coefficients in the balanced equation).
Then g Li = mols Li x atomic mass Li = ?
To determine the mass of lithium required to react completely with 57.5 mL of N2 gas at STP, we need to use the stoichiometry of the balanced chemical equation given.
Let's start by converting the volume of N2 gas to the number of moles. We can use the ideal gas law:
PV = nRT
At STP (Standard Temperature and Pressure), the values are:
- Pressure (P) = 1 atm
- Volume (V) = 57.5 mL = 0.0575 L (convert to liters)
- Temperature (T) = 273.15 K
- Gas constant (R) = 0.0821 L·atm/(mol·K)
Using the ideal gas law, we can solve for moles of N2 (n):
n = PV / RT
n = (1 atm) * (0.0575 L) / (0.0821 L·atm/(mol·K) * 273.15 K)
Now, let's calculate the moles of N2 gas:
n = 0.0575 / (0.0821 * 273.15)
Next, we need to use the stoichiometry of the balanced chemical equation to find the moles of lithium required. According to the balanced equation:
6Li(s) + N2(g) → 2Li3N(s)
From the equation, we can see that 6 moles of Li react with 1 mole of N2. Therefore, the number of moles of lithium required is:
moles of Li = (moles of N2) * (6 moles of Li / 1 mole of N2)
Finally, to convert the moles of lithium to grams, we need to use the molar mass of lithium (6.94 g/mol). Multiply the moles of Li by the molar mass to obtain the mass of lithium required.
mass of Li = (moles of Li) * (molar mass of Li)
With these calculations, you can find the mass of lithium required to react completely with 57.5 mL of N2 gas at STP.
To determine the mass of lithium required to react completely with the given volume of N2 gas at STP (Standard Temperature and Pressure), we need to follow these steps:
1. Write and balance the chemical equation:
6Li(s) + N2(g) → 2Li3N(s)
2. Find the molar volume of any gas at STP:
At STP, one mole of any gas occupies 22.4 L of volume. Therefore, 22.4 L of N2 gas corresponds to 1 mole of N2.
3. Convert the given volume of N2 gas to moles:
We are given 57.5 mL of N2 gas. Since 1 L = 1000 mL, we can convert:
57.5 mL ÷ 1000 mL/L = 0.0575 L
Now, we can calculate the moles of N2 gas:
Moles of N2 = volume of N2 gas / molar volume of N2 at STP
Moles of N2 = 0.0575 L / 22.4 L/mol ≈ 0.0026 mol
4. Use the stoichiometry of the balanced equation to determine the moles of lithium:
From the balanced equation, for every 1 mole of N2 gas, we need 6 moles of Li.
Moles of Li = moles of N2 gas × (6 moles of Li / 1 mole of N2 gas)
Moles of Li = 0.0026 mol × 6 ≈ 0.0156 mol
5. Calculate the mass of lithium using its molar mass:
The molar mass of lithium (Li) is approximately 6.94 g/mol.
Mass of Li = moles of Li × molar mass of Li
Mass of Li = 0.0156 mol × 6.94 g/mol ≈ 0.108 g
Therefore, approximately 0.108 grams of lithium (Li) are required to react completely with 57.5 mL of N2 gas at STP.