Consider the following chemical equation : 2NO2(g)=N2O4(g). If 25.0mL of NO2 gas is completely converted to N2O4 gas under the same conditions, what volume will the N2O4 occupy?
25.0 mL NO2 x (1 mol N2O4/2 mols NO2) = 25.0 x 1/2 = ?
This is a short cut in which volume is used as if it were mols. You can do that since the conditions are the same .
To solve this problem, we need to use the molar volume concept, which states that equal volumes of gases, at the same temperature and pressure, contain the same number of molecules.
First, let's calculate the number of moles of NO2 gas we have:
Given that we have 25.0 mL of NO2 gas, we should convert it to liters by dividing by 1000:
25.0 mL / 1000 mL/L = 0.0250 L
Next, we need to convert the volume of NO2 gas to moles using the ideal gas law equation:
PV = nRT
Where:
P = pressure (constant)
V = volume
n = moles of gas
R = ideal gas constant
T = temperature (constant)
Since both reactions occur under the same conditions, the pressure (P), temperature (T), and ideal gas constant (R) will be the same for both gases.
Therefore, the ratio of moles of NO2 to moles of N2O4 is:
2 mol NO2 : 1 mol N2O4
0.0250 L NO2 * (2 mol NO2 / 1 L NO2) = 0.050 mol NO2
According to the stoichiometry of the chemical equation, for every 2 moles of NO2, we obtain 1 mole of N2O4.
So, 0.050 mol NO2 * (1 mol N2O4 / 2 mol NO2) = 0.025 mol N2O4
Finally, we can calculate the volume of N2O4 gas produced by converting moles to liters using the ideal gas law:
PV = nRT
V = nRT / P
Assuming the pressure and temperature are constant, we can write:
V(N2O4) = (0.025 mol N2O4 * R * T) / P
Since the number of moles (n) and the ideal gas constant (R) are constant, we can simplify the equation to:
V(N2O4) = constant / P
Therefore, the volume of N2O4 gas produced will be directly proportional to the pressure.
Now, we don't have the pressure value, so we cannot calculate the exact volume of N2O4 gas. We will need to know the pressure to determine its volume.
I hope this helps!
To find the volume of N2O4 gas, we need to use the stoichiometry of the chemical equation. The coefficients of the balanced equation represent the mole ratio between reactants and products. In this case, the coefficient of NO2 is 2, and the coefficient of N2O4 is also 2.
Given that 25.0 mL of NO2 is completely converted, we need to find the volume of N2O4 gas.
Step 1: Convert the volume of NO2 from milliliters (mL) to liters (L).
25.0 mL × (1 L/1000 mL) = 0.025 L
Step 2: Use the mole ratio from the balanced equation to find the moles of N2O4.
Since the moles of NO2 and N2O4 are the same (coefficient ratio of 2:2), the moles of N2O4 is also 0.025.
Step 3: Convert the moles of N2O4 to volume in liters by using the ideal gas law equation.
PV = nRT
Assuming the conditions are constant (same pressure, temperature, and ideal gas behavior), we can solve for V (volume) by rearranging the equation:
V = nRT / P
Given:
n = 0.025 moles (from step 2)
R = 0.0821 L·atm/mol·K (Gas constant)
P = constant pressure (not given in the question)
Since the pressure is not given, we can assume it to be 1 atm for simplicity.
V = (0.025 mol)(0.0821 L·atm/mol·K)(298 K) / (1 atm)
V = 0.610 L
Therefore, the volume of N2O4 gas, under the same conditions as NO2 gas, will be approximately 0.610 liters.