Could you show me where to start on solving this equation?
The reaction in question will be carried out in a calorimeter. The volume of the chamber inside is 2.00 L. Experiment starts by evacuating the chamber to 0.00 kPa. Then oxygen gas is filled into the chamber till pressure 200. kPa. Then hydrogen gas is filled into the same chamber until total pressure 400. kPa. The oxygen and hydrogen mixture is ignited by a spark with 3.00 kJ energy. Calculate the total pressure inside the chamber after reaction.
Bob Pursley answered this just a day or so ago but I can't find it or I would give you a link. Here is how to do it.
First you need to determine the limiting reagent.
H2 will require 100 kPa O2 to react completely; you have that much so H2 must be the limiting reagent. Next, you aren't given mols but you have P. In PV = nRT, T isn't given but it is constant, R is a constant, volume isn't given but it is constant. That means P is proportional to n; therefore, we can use kPa pressure as if it were mols.
.....2H2 + O2 ==> 2H2O
I....200...200.....0
C...-200..-100....+200
E.....0....100....200
So total P is 100 + 200 = ?kPa.
To solve this problem, we need to use the ideal gas law equation, which states:
PV = nRT
where:
P is the pressure of the gas (in kPa)
V is the volume of the chamber (in L)
n is the number of moles of gas
R is the ideal gas constant (0.0821 L·atm/(mol·K))
T is the temperature of the gas (in Kelvin)
First, let's convert the given pressures to atmospheres (atm):
200 kPa = 200/101.325 = 1.97 atm
400 kPa = 400/101.325 = 3.95 atm
Since we know the total volume is 2.00 L, we can find the number of moles of oxygen gas using the ideal gas law. Rearranging the equation to solve for n, we have:
n = PV / RT
Substituting the values, we get:
n(oxygen) = (1.97 atm * 2.00 L) / (0.0821 L·atm/(mol·K) * T)
Next, let's find the number of moles of hydrogen gas. Since the oxygen and hydrogen gases are mixed in a 1:2 ratio (stoichiometric ratio), the moles of hydrogen gas will be twice the moles of oxygen gas:
n(hydrogen) = 2 * n(oxygen)
Now, we can find the total number of moles before the reaction:
n(total) = n(oxygen) + n(hydrogen)
After the reaction occurs and the spark ignites, the energy released (3.00 kJ) will increase the temperature of the gas. However, since we are not given any information about the final temperature, we assume the temperature remains constant. Therefore, the number of moles, volume, and the ideal gas constant remain the same after the reaction. We can use the ideal gas law again to find the final pressure (P(final)) inside the chamber:
P(final) = n(total) * R * T / V
Since T (temperature) and V (volume) are constant, we can plug in the known values to calculate P(final).