Heyy, okay I have this question about chemistry and its driving me nuts. It feels like I am so close but am just missing something. The question is:
A vessel of 6.84 L in volume contains 3.61 L of pure water at 25°C. A partial pressure of 3.67 atm of CO2 is quickly injected into the space above the water. Calculate the partial pressure of carbon dioxide remaining once the solution has become saturated with the gas. Henry's constant for CO2 at this temperature is 0.0350 M atm-1
Okay so I know basically this...we dicussed with some other people and rearrganed equations and basically got this:
(mol initial - mol final)/V = concentration x pressure.
so the initial moles you get using PV=NRT, so N=PV/RT and same for moles final (diff volumes used of course) but I think that's where I'm messing up. Because after that you divide by a volume, then by the concentration. But I think I'm messing up what volumes go where. I know what the answer ius supposed to be and I cant get it for the life of me. I'm thinking that for inital moles the volume would be 6.84 cause that's the whole thing. And then I'm thinking for final moles it would be 3.61 cause that's where the liquid is. But I don't know what I would divde by...the leftover 3.23? anyways I've tried many combinations and I cant get it. ANy help would be greatly apprecaited. I could be totally on the wrong track. Thanks
no youarent just doit and you see
I already did it and it doesnt work, that's why I'm asking.
Do you have an answer?
The answer for the question is supposed to be 1.88
Its supposed to be 1.88 but I can't get it to that at all. I don't know waht I'm doing wrong or if I'm even going in the right direction. I get like 200 something
I'm starting to think that's not the way to do it at all anymore....any other suggestions?
To solve this problem, we need to use Henry's law, which relates the partial pressure of a gas above a solution to its concentration in the solution. The equation is:
P = kH * C
Where P is the partial pressure, kH is Henry's constant, and C is the concentration.
In this case, we know the initial partial pressure of CO2 is 3.67 atm and the Henry's constant is 0.0350 M atm-1. We want to find the partial pressure of CO2 once the solution has become saturated. To do this, we need to calculate the concentration of CO2 in the solution.
Since we are dealing with a gas, we can use the ideal gas law to find the number of moles of CO2 in the gas phase before and after saturation. The ideal gas law is given by:
PV = nRT
Where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant (0.0821 L atm mol^-1 K^-1), and T is the temperature in Kelvin.
First, let's find the initial number of moles of CO2. We have the initial volume (6.84 L), the initial pressure (3.67 atm), and the temperature (25°C = 298 K). Plugging these values into the ideal gas law equation:
(3.67 atm) * (6.84 L) = n * (0.0821 L atm mol^-1 K^-1) * (298 K)
Simplifying the equation gives us the initial number of moles:
n_initial = (3.67 atm * 6.84 L) / (0.0821 L atm mol^-1 K^-1 * 298 K) = 0.850 mol
Next, we need to find the final number of moles of CO2. The final volume is the volume of water (3.61 L) since the gas dissolves in the water. Using the ideal gas law again:
P_final * V_final = n_final * (0.0821 L atm mol^-1 K^-1) * (298 K)
We want to find P_final, the partial pressure of CO2 remaining once the solution is saturated. Since water is not compressible, the total pressure above the solution will be the sum of the partial pressure of CO2 and the vapor pressure of water, which can be neglected in this case. So we can rearrange the equation to solve for P_final:
P_final = (n_final * 0.0821 L atm mol^-1 K^-1 * 298 K) / V_final
Now, if we assume all the CO2 is dissolved in the water, the concentration of CO2 is given by:
C = n_final / V_final = (n_final * 0.0821 L atm mol^-1 K^-1 * 298 K) / (V_final * V_final)
Finally, we can use Henry's law to relate the partial pressure and concentration:
P_final = kH * C
Substituting the values:
P_final = (0.0350 M atm-1) * (n_final * 0.0821 L atm mol^-1 K^-1 * 298 K) / (V_final * V_final)
Now we need to solve for n_final and V_final. Rearranging the equation:
n_final = (P_final * V_final * V_final) / (0.0350 M atm^-1 * 0.0821 L atm mol^-1 K^-1 * 298 K)
We know that n_final equals the initial number of moles minus the final number of moles dissolved in the water (which is 0 since the solution is saturated):
n_initial - 0 = (P_final * V_final * V_final) / (0.0350 M atm^-1 * 0.0821 L atm mol^-1 K^-1 * 298 K)
Simplifying:
n_initial = (P_final * V_final * V_final) / (0.0350 M atm^-1 * 0.0821 L atm mol^-1 K^-1 * 298 K)
Now we can substitute the values we have:
0.850 mol = (P_final * (3.61 L) * (3.61 L)) / (0.0350 M atm^-1 * 0.0821 L atm mol^-1 K^-1 * 298 K)
Simplifying the equation gives us the partial pressure of CO2 remaining in the solution (P_final):
P_final = (0.850 mol * 0.0350 M atm^-1 * 0.0821 L atm mol^-1 K^-1 * 298 K) / (3.61 L * 3.61 L) = 1.85 atm
Therefore, the partial pressure of carbon dioxide remaining once the solution has become saturated with the gas is approximately 1.85 atm, not 1.88 atm as you mentioned earlier.