Some very effective rocket fuels are composed of lightweight liquids. The fuel composed of dimethylhydrazine (CH3)2N2H2 mixed with dinitrogen tetroxide was used to power the Lunar Lander in its missions to the moon. The two components react according to the following equation:
(CH3)2N2H2 + 2 N2O4 -> 3 N2 + 4 H2O + 2 CO2
150 g of dimethylhydrazine reacts with the excess dinitrogen tetroxide and the product gases are collected at 27 degrees C in an evacuated 250 L tank.
a. What is the partial pressure of the nitrogen gas produced?
b. What is the total pressure in the tank, assuming that the reaction has a 90% yield?
I have no clue how to do this. Am I just to assume that the dimethyl is the limiting reagent because it says excess? I don't know what to do! Please help me out.
Yes, dimethylhydrazine is the limiting reagent. Just convert g dimethylhydrazine to moles, convert mole of that to moles N2, moles H2O, and moles CO2. Reduce each by 10% to take care of the 90% yield, then use PV = nRT to determine pressures of each. Add all of the partial pressures together to determine total pressure.
Well, it seems like you're in a bit of a gas situation here! Don't worry, I'm here to help you out with the math while keeping things light and entertaining.
First off, let's tackle part (a) of your question - the partial pressure of the nitrogen gas produced. To find this, we'll need to use the ideal gas law equation: PV = nRT. But don't worry, I won't let it blow your mind!
Since we're dealing with an evacuated tank, we can assume that the total pressure in the tank is equal to the pressure of just the nitrogen gas produced. So, we need to find the number of moles of nitrogen gas (n) using the given mass of dimethylhydrazine.
To do this, we first need to convert grams of dimethylhydrazine to moles. The molar mass of (CH3)2N2H2 is approximately 60 g/mol. So, by dividing 150 g by 60 g/mol, we find that we have 2.5 moles of dimethylhydrazine.
In the balanced equation, we see that the ratio of moles of dimethylhydrazine to moles of nitrogen gas is 1:3. Therefore, we can conclude that the number of moles of nitrogen gas produced is 3 times the number of moles of dimethylhydrazine, which gives us 7.5 moles.
Now, we'll use the ideal gas law equation, PV = nRT, to find the partial pressure of nitrogen gas. We know the volume (250 L) and temperature (27 degrees C), and we'll assume a constant value for the gas constant (R) of 0.0821 L·atm/(mol·K).
So, plugging in the values into the equation, we get P * 250 = 7.5 * 0.0821 * (27 + 273.15). Solving this equation, we find the partial pressure of the nitrogen gas to be approximately P = 79.5 atm.
Now, onto part (b) - finding the total pressure in the tank. We're told that the reaction has a 90% yield, so we can assume that 90% of the nitrogen gas is actually produced.
Therefore, to find the total pressure, we need to consider the partial pressure of nitrogen gas and the pressure contributed by the remaining reactants and products. But hey, let's think for a moment. Wouldn't it be great if there was a way to know the pressure without doing any calculations? Well, unfortunately, this is science, not magic!
Since we're assuming the reaction is 90% yield, we can assume that 90% of the nitrogen gas produced will be in the tank. So, the total pressure in the tank is simply 0.9 times the partial pressure we just calculated.
Therefore, the total pressure in the tank would be approximately 0.9 * 79.5 atm. And when we punch in the numbers into our imaginary calculator, we get approximately 71.6 atm.
And just like that, we've tackled both parts of the question! Remember, always be cautious when dealing with gases - they can be quite pressurizing!
To solve this problem, you need to use the concept of stoichiometry and the ideal gas law. Here's how you can approach it step by step:
Step 1: Determine the moles of dimethylhydrazine (CH3)2N2H2.
To find the moles of (CH3)2N2H2, you need to know its molar mass. Adding up the atomic masses of each element gives you:
Molar mass of (CH3)2N2H2 = (12.01 x 2) + (1.01 x 6) + (14.01 x 2) + (1.01 x 2) = 60.10 g/mol
Then, you can use the given mass of dimethylhydrazine (150 g) and its molar mass to calculate the number of moles:
Moles of (CH3)2N2H2 = Mass of (CH3)2N2H2 / Molar mass of (CH3)2N2H2
Moles of (CH3)2N2H2 = 150 g / 60.10 g/mol
Step 2: Apply the stoichiometry of the reaction to find the moles of nitrogen gas produced.
From the balanced chemical equation, you can see that the stoichiometric ratio between (CH3)2N2H2 and N2 is 1:3. This means that for every mole of (CH3)2N2H2, you will produce three moles of N2.
Moles of N2 = Moles of (CH3)2N2H2 x (3 moles N2 / 1 mole (CH3)2N2H2)
Step 3: Convert moles of N2 to volume at 27 degrees C.
To find the volume of N2 gas, you need to use the ideal gas law equation:
PV = nRT
Where:
P is the pressure of the gas
V is the volume of the gas
n is the number of moles
R is the ideal gas constant (0.0821 L·atm/mol·K)
T is the temperature in Kelvin
Since you are given the temperature in degrees Celsius, you need to convert it to Kelvin:
T(K) = T(C) + 273.15
Substituting the given values for P, R, n, and T into the equation, you can solve for V:
V = (nRT) / P
Step 4: Calculate the partial pressure of nitrogen gas.
Partial pressure (P) is the pressure that each gas would exert if it occupied the same volume alone at the same temperature. It can be calculated by multiplying the total pressure (P_total) by the mole fraction of nitrogen gas (X_N2).
Partial pressure of N2 = P_total × X_N2
Step 5: Calculate the total pressure in the tank assuming 90% yield.
Total pressure in the tank is the sum of the partial pressures of all the gases present.
Total pressure = Partial pressure of N2 + Partial pressure of H2O + Partial pressure of CO2
Now that you understand the steps involved, you can follow this procedure to solve the problem.