To determine the final volume of gas, we first need to understand the stoichiometry of the reaction between nitrogen gas (N2) and hydrogen gas (H2) to form ammonia gas (NH3). According to the balanced chemical equation:
N2 + 3H2 → 2NH3
From the equation, we can see that for every 1 mole of N2, we need 3 moles of H2 to produce 2 moles of NH3. Using this information, we can calculate the final volume.
a) What is the final volume of gas?
Since we are given the initial volume of N2 as 1.0 L, we can use the stoichiometry to determine the volumes of H2 and NH3.
From the balanced equation, for every 1 L of N2, 3 L of H2 are required. So, if we started with 1.0 L of N2, we would need 3.0 L of H2.
Next, we need to determine the volume of NH3 produced. From the equation, 2 moles of NH3 are produced for every 1 mole of N2. Since the volume ratios are the same as the mole ratios, we can convert the volume of N2 to moles and then convert to the volume of NH3.
Using the ideal gas law equation 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, we can calculate the number of moles of N2:
n(N2) = PV/(RT) = (1.0 L)(1 atm)/(0.0821 L·atm/mol·K)(T)
Similarly, we can calculate the number of moles of NH3:
n(NH3) = (2 moles N2/1 mole NH3) * n(N2)
To find the final volume of NH3, we can use the ideal gas law again:
V(NH3) = n(NH3)RT/P
Note: The pressure and temperature must remain constant throughout the reaction for these calculations to be valid.
b) 5.0 L of N2 + 9.0 L H2. What final volume?
Using the same approach, we can determine the final volume of gas produced when 5.0 L of N2 and 9.0 L of H2 react. Based on the stoichiometry, we can determine the volume of NH3 produced.
First, we calculate the moles of N2 and H2:
n(N2) = PV/(RT) = (5.0 L)(1 atm)/(0.0821 L·atm/mol·K)(T)
n(H2) = PV/(RT) = (9.0 L)(1 atm)/(0.0821 L·atm/mol·K)(T)
Based on the balanced equation, 2 moles of NH3 are produced for every 1 mole of N2. So, we can determine the number of moles of NH3:
n(NH3) = (2 moles N2/1 mole NH3) * n(N2)
Finally, using the ideal gas law, we calculate the volume of NH3:
V(NH3) = n(NH3)RT/P
Remember to use the same pressure and temperature conditions throughout the calculations for accuracy.