A sample of NH4HS(s) is placed in a 2.61 −L flask containing 0.120 mol NH3(g).
NH4HS(s)⇌NH3(g)+H2S(g) KP=0.108 at 25∘C
What will be the total gas pressure when equilibrium is established at 25∘C?
Express your answer using four significant figures.
I've done
PV=nRT
P= nRT/V
P= (0.120mol)(0.08206 L.atm/K.mol)(25+273K) / (2.61L)
NH4HS(s)⇌NH3(g)+H2S(g)
I - 1.124 0
C - +x +x
E - 1.124+x x
0.108= x(1.124+x)
x^2 +1.124x-0.108=0
x1 = 0.08903 x2= -1.2136
P total gas = 0.08903 + 1.124 = 1.2130
Did I do something wrong? Any help would be greatly appreciated. Thx
answer to four sig digits. Wondering what to four sig digits for 273 in temp will change. I dont see any other red flags.
First off you made a math error.
x = 0.08903. Right. But you added that in once and not twice.
Total P = 1.124 + 0.08903 + 0.08903 = 1.302 using T as 298. Using T as 298.15 may change that last place but I didn't go through the math.
Another point you may check is Kp. Is that Kp or Kc. You don't have it in the problem you posted anywhere that I can see. Also, read your problem and check that you copied the number correctly.
From your calculations, it seems like you made a small error in determining the value of x. Let's go through the calculations together to identify the mistake.
To find the value of x, we need to solve the quadratic equation:
x^2 + 1.124x - 0.108 = 0
Using the quadratic formula, x = (-b ± √(b^2 - 4ac)) / (2a), where a = 1, b = 1.124, and c = -0.108.
Calculating the discriminant, √(b^2 - 4ac) = √(1.124^2 - 4(1)(-0.108)) = √(1.262624) ≈ 1.123
Now applying the quadratic formula:
x = (-1.124 ± 1.123) / 2
x1 = (-1.124 + 1.123) / 2 ≈ 0.0005
x2 = (-1.124 - 1.123) / 2 ≈ -1.1235
Since we are talking about the concentration of gases, it doesn't make sense for x to have a negative value. Therefore, x = 0.0005 is the correct value.
Now, to find the total gas pressure, you need to add the partial pressures of NH3 and H2S:
P_total gas = P_NH3 + P_H2S
At equilibrium, the mole ratio between NH3 and NH4HS is 1:1, so the partial pressure of NH3 will be (1.124 mol + x) = 1.1245 atmospheres.
Since the molar ratio between H2S and NH4HS is also 1:1, the partial pressure of H2S will also be x = 0.0005 atmospheres.
Therefore:
P_total gas = 1.1245 + 0.0005 = 1.125 atmospheres
So the correct answer for the total gas pressure, expressed with four significant figures, is 1.125 atm.
I hope this clarifies your doubts and helps you understand the correct calculation. Let me know if you have any further questions!