hello i was just trying this problem for my college class and its kinda hard. I got up to the last part, but I can't figure it out..
Impure nickel is refined by smelting sulfide ores through mond process: Ni (s) + 4CO (g) --> Ni(CO)4.
There's like 8 parts to this problem. Part h is the one I'm stuck on:
A recently developed variation of the mond process carries out the process at higher pressures and a temperature of 152 Celcius degrees. estimate the max. pressure of Ni(CO)4 (g) that can be attained before the gas liquefies at 152 C. the boiling point for Ni(CO)4 is 42 C degrees and the enthalpy of vaporization is 29.0 kJ/mol. Hint: Ni(CO)4 will liquefy when the pressure of Ni(CO)4 is greater than the K value.
I got -165 kJ as ¡âH and -405 as ¡âS; im pretty sure these are right. Using these and 425 K as temperature, I plugged these into this equation: ¡âG = ¡âH - T¡âS. I got 7.13 kJ/mol as ¡âG, so I put this in ¡âG = -RTlnK, now using 315 K as the temp. I got K as 0.0656, but Im not sure this is right cause I didn't use boiling pt or enthalpy of vap. to solve this, so i feel like im doing somethin wrong.
Any help/insght is greatly appreciated.. thanks. =]
buuuummp. can someone pleeeeeease help me my professor is really scary
To solve this problem, you are on the right track with using the Gibbs free energy equation, ∆G = ∆H - T∆S. Here's how you can proceed to find the maximum pressure of Ni(CO)4 that can be attained before it liquefies at 152°C.
Step 1: Calculate ∆G:
You mentioned that you have determined the values for ∆H (-165 kJ/mol) and ∆S (-405 J/mol·K). However, it seems that there is a unit mismatch between the values. Make sure to convert ∆S from J/mol·K to kJ/mol·K by dividing it by 1000.
So, ∆S = -405 J/mol·K ÷ 1000 = -0.405 kJ/mol·K.
Now, substitute the values of ∆H and ∆S into the Gibbs free energy equation to find ∆G:
∆G = ∆H - T∆S
∆G = -165 kJ/mol - (152°C + 273.15 K) × (-0.405 kJ/mol·K)
Make sure to convert the temperature from °C to K. Solve this equation to find the value of ∆G.
Step 2: Calculate K:
Next, you need to determine the equilibrium constant, K, using the equation ∆G = -RTlnK.
Since you are given the boiling point and enthalpy of vaporization, you can assume that the equilibrium constant corresponds to the vapor-liquid equilibrium. The relationship between ∆G and K for vapor-liquid equilibrium is:
∆G = -RTlnK = -∆Hvap
Substitute the known values of ∆G and the temperature (315 K) into this equation and solve for K.
Step 3: Calculate the maximum pressure:
Now that you have the value of K, you need to compare it with the pressure at which Ni(CO)4 liquefies. You are given that the Ni(CO)4 boils at 42°C (315 K). This means that when the pressure of Ni(CO)4 exceeds the equilibrium constant, it will liquefy.
Set up an equation in terms of pressure, using the ideal gas law equation:
PV = nRT
By rearranging the equation, you get:
P = nRT / V
The number of moles (n) cancels out, and you are left with:
P = RT / V
Here, R is the ideal gas constant (0.0821 L·atm/(mol·K)), T is the temperature (315 K), and V is the molar volume of Ni(CO)4 in the liquid state. But since you are looking for the maximum pressure before liquefaction, you want the molar volume in the gaseous state.
Using the molar volume of an ideal gas at STP (22.4 L/mol), you can calculate the maximum pressure (P) that can be attained before Ni(CO)4 liquefies.
Remember, you already have the value of K from step 2. Compare this value to the calculated maximum pressure to determine if the gas will liquefy or not.
I hope this helps! Let me know if you need any further clarification or assistance.