What pressure would have to be applied to steam at 325°C to condense the steam to liquid water (ÄH vap = 40.7 kJ/mol)?
Responses
Dr bob please! Chemistry - GK, Friday, November 28, 2008 at 11:47pm
Use the Clausius-Clapeyron Equation to calculate the vapor pressure at 325°C. That is the pressure that must be applied to condense the steam at 325°C.
Ln(P2/P1) = (∆H/R)[(T2-T1)/T2T1]
P1 = 1 atm
∆H = 40700J
R = 8.3145 J/°K.mol
T2 = (325+273) = 598°K
T1 = (100+273) = 373°K
P2 = (unknown)
[NOTE: The pressure needed is quite high]
Dr bob please! Chemistry - Rachelle, Sunday, November 30, 2008 at 10:06pm
i solved for lnx=4,852,725
whats next? and i relaly cant put it into the calc. it says (overflow)
You must be punching the calculator wrong somewhere. By the way that was GK that gave you that answer in such nice detail. I worked the problem and end up with
ln P2 = 4.93777 and when I click on ex I get an answer. Your digits are about the same but the decimal point is way different.
If you want to type in your set up and the follow through I will check it for you step by step.
Well, it seems like you have a bit of a steamy situation on your hands! Don't fret though, I'm here to help (and make you laugh along the way).
Now, if you'd like to calculate the pressure needed to condense steam at 325°C, you can use the Clausius-Clapeyron Equation. But be warned, the pressure needed is quite high, so hold on tight!
According to Dr. Bob's equation, ln(P2/P1) = (∆H/R)[(T2-T1)/T2T1]. Now, I'm not a mathematician, but I have to say, that equation looks a bit like alphabet soup!
But no worries, let's break it down. P1 is equal to 1 atmosphere (or your average air pressure). ∆H is the enthalpy change, which in this case is 40.7 kJ/mol, or as I like to call it, "a whole lot of energy". R is a fancy constant (8.3145 J/°K.mol) that likes to hang out in equations, and T2 and T1 are your temperatures in Kelvin.
So, plug in those numbers and solve for lnx. Now, if you're getting an "overflow" error on your calculator, it's time to call in the professionals. I'm just a clown bot, after all!
But don't worry, with a little tinkering and a lot of patience, I'm sure you'll get that answer in no time. Just remember to handle the pressure with a sense of humor!
To solve the equation ln(P2/P1) = (∆H/R)[(T2-T1)/T2T1], you need to rearrange it to solve for P2:
ln(P2/P1) = (∆H/R)[(T2-T1)/T2T1]
P2/P1 = e^[(∆H/R)[(T2-T1)/T2T1]]
P2 = P1 * e^[(∆H/R)[(T2-T1)/T2T1]]
Now, you can plug in the values into the equation:
P1 = 1 atm
∆H = 40.7 kJ/mol = 40,700 J/mol
R = 8.3145 J/(°K mol)
T2 = 325°C + 273.15 = 598.15 K
T1 = 100°C + 273.15 = 373.15 K
P2 = 1 atm * e^[((40,700 J/mol) / (8.3145 J/(°K mol))) * ((598.15 K - 373.15 K) / (598.15 K * 373.15 K))]
Now you can calculate P2 using a calculator or an online tool that can handle large exponential calculations.
To find the pressure that needs to be applied to steam at 325°C to condense it to liquid water, you can use the Clausius-Clapeyron Equation. Here's how you can solve it step by step:
1. First, convert the given enthalpy change (ΔH) from kilojoules per mole to joules per mole. ΔH = 40.7 kJ/mol = 40,700 J/mol.
2. Next, convert the temperatures from Celsius to Kelvin. T2 = 325°C + 273.15 = 598.15 K (temperature at which you want to condense the steam), and T1 = 100°C + 273.15 = 373.15 K (boiling point of water at 1 atm).
3. Plug the values into the Clausius-Clapeyron Equation: ln(P2/P1) = (ΔH/R)((T2-T1)/(T2*T1)), where P1 is the vapor pressure at T1 (which is 1 atm), R is the ideal gas constant (8.3145 J/(K*mol)), T2 and T1 are the temperatures calculated in the previous step, and P2 is the unknown pressure you need to find.
4. Rearrange the equation to solve for P2. Take the exponential of both sides of the equation: P2/P1 = e^((ΔH/R)((T2-T1)/(T2*T1))).
5. Substitute the known values and calculate P2: P2/1 atm = e^((40,700 J/mol)/(8.3145 J/(K*mol)) * ((598.15 K - 373.15 K) / (598.15 K * 373.15 K)).
6. Evaluate the exponential term using a calculator or a computer program. It seems like the value of the exponential is very large, which might cause an "overflow" error on a regular calculator.
In this case, using a scientific calculator or a computational software that can handle large numbers is recommended. You can try using the natural logarithm (ln) function of a calculator to calculate the natural logarithm of the exponential term, and then raise e to that value to get the result.
Please note that the pressure needed to condense the steam at 325°C is expected to be quite high.