Nitric acid can be produced by the reaction of
gaseous nitrogen dioxide with water.
3NO2(g) + H2O(`) −!
2HNO3(`) + NO(g)
If 745 L of NO2 gas react with water, what
volume of NO gas will be produced? As-
sume the gases are measured under the same
conditions.
Convert 745 L NO2 to L NO using the coefficients in the balanced equation.
? L NO ==> 745 L NO2 x (1 mole NO/3 mol NO2) = 745L x 1/3 = ?
To determine the volume of NO gas produced, we need to use the molar ratios from the balanced equation. Let's break down the steps to solve this problem:
Step 1: Write down the balanced equation:
3NO2(g) + H2O(`) −! 2HNO3(`) + NO(g)
Step 2: Determine the number of moles of NO2 involved:
Use the ideal gas law equation, PV = nRT, where:
P = pressure (assumed to be constant)
V = volume of NO2 (745 L)
n = number of moles of NO2
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature (assumed to be constant)
Since the volume is provided in liters and we need the number of moles, we rearrange the equation to solve for n:
n = PV / RT
Step 3: Calculate the number of moles of NO2:
Using the given values:
P = 1 atm (assuming the pressure is 1 atmosphere)
V = 745 L
R = 0.0821 L·atm/mol·K
Assume T = 298 K (room temperature)
n = (1 atm * 745 L) / (0.0821 L·atm/mol·K * 298 K)
Solve for n to find the number of moles of NO2.
Step 4: Use the stoichiometry ratios to find the number of moles of NO produced:
From the balanced equation, the stoichiometry tells us that for every 3 moles of NO2 reacting, 1 mole of NO is produced.
Therefore, the number of moles of NO produced is n/3.
Step 5: Convert moles of NO to volume:
Using the ideal gas law again:
n = PV / RT
Assuming the same conditions as before (P = 1 atm, R = 0.0821 L·atm/mol·K, T = 298 K), we can calculate the volume of NO gas produced.
Step 6: Convert volume to liters:
Convert the number of moles of NO to liters using the molar volume of gas at standard temperature and pressure (STP), which is 22.4 L/mol.
Multiply the number of moles of NO by the molar volume (22.4 L/mol) to find the volume in liters.
Following these steps, you should be able to determine the volume of NO gas produced.