Nitric acid can be produced by the reaction of
gaseous nitrogen dioxide with water.
3 NO2(g) + H2O(ℓ) −→
2 HNO3(ℓ) + NO(g)
If 734 L of NO2 gas react with water, what
volume of NO gas will be produced? Assume
the gases are measured under the same
conditions.
Answer in units of L
When using gases one can take a shortcut and use volume as if it were mols.
734 L NO2 x (1 mol NO/3 molls NO2) = 734 x 1/3 = ?
To determine the volume of NO gas produced, we need to use the stoichiometry of the balanced chemical equation.
From the balanced equation, we can see that the ratio of the coefficients between NO2 and NO is 1:1. This means that for every 1 mole of NO2 reacted, 1 mole of NO is produced.
First, we need to convert the volume of NO2 gas to moles using the ideal gas law equation:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature
Since the pressure, temperature, and conditions are the same for both gases, we can simplify the equation to:
V(NO2) = n(NO2) * (RT / P)
Given that the volume of NO2 gas is 734 L, we can calculate the number of moles of NO2 using the equation:
n(NO2) = V(NO2) * (P / RT)
Now, since the stoichiometric ratio of NO2 to NO is 1:1, the number of moles of NO produced is also 734 moles.
Finally, we can use the ideal gas law equation again to calculate the volume of NO gas:
V(NO) = n(NO) * (RT/P)
Substituting the values:
V(NO) = 734 moles * (RT / P)
The volume of NO gas produced is therefore 734 L.
To determine the volume of NO gas produced, we need to use the stoichiometry of the balanced chemical equation. The coefficients in the balanced equation represent the molar ratios between the reactants and products.
From the balanced equation:
3 NO2(g) + H2O(ℓ) → 2 HNO3(ℓ) + NO(g)
We can see that for every 3 moles of NO2 reacted, 1 mole of NO is produced. Therefore, the molar ratio between NO2 and NO is 3:1.
To solve this problem, we can follow these steps:
Step 1: Convert the given volume of NO2 gas to moles.
To convert the volume of gas to moles, we need to use the ideal gas law equation:
PV = nRT
Where:
P = pressure (assumed to be constant)
V = volume of gas (734 L)
n = number of moles
R = ideal gas constant
T = temperature (assumed to be constant)
Since the conditions are the same for both gases, we can consider the pressure, temperature, and ideal gas constant as constant values. Thus, we can disregard them for this calculation.
Step 2: Use the molar ratio to calculate the moles of NO gas produced.
Using the molar ratio of 3:1 from the balanced equation, we can set up the following proportion:
3 moles NO2 / 1 mole NO
Since we calculated the moles of NO2 in Step 1, we can use this proportion to determine the moles of NO gas produced.
Step 3: Convert the moles of NO gas to volume.
To convert moles of gas to volume, we need to use the same ideal gas law equation as mentioned in Step 1.
PV = nRT
Since the pressure, temperature, and ideal gas constant are the same for both gases, we can assume they cancel each other out. Thus, it is safe to say that the volume is directly proportional to the number of moles.
Step 4: Calculate the volume of NO gas.
Using the calculated moles of NO gas and the proportionality between moles and volume, we can determine the volume of NO gas produced.
Finally, plug in the values and solve for the volume of NO gas produced.
Keep in mind that this method assumes the reaction goes to completion and all the given NO2 gas reacts.