CH2==Ch2(g) ----> CH4(g) + C (graphite)
If the decomposition begina at 10 degrees C and 50.0 atm with a gas density of 0.215 g/mL and the temperature increases by 950K, what is the final pressure of the confined gas (ignore the volume of graphite and use the van der waals equation)
So what's your problem? Just plug into the van der Waals equation.
I don't know how to throw density into the equation.
scratch that.. i really don't get any of it. formula I have is: (P + (n^2a)/V^2)(V-nb) = nRT
what I can fill in is (P + (n^2(2.25))/V^2)(V-n(.0428)) = n(.0821)(950)
To find the final pressure of the confined gas using the van der Waals equation, we need to take into account the initial conditions and the temperature change.
1. Write out the balanced equation of the reaction: CH2 == Ch2(g) → CH4(g) + C (graphite)
2. Determine the initial conditions:
- Initial temperature (T1) = 10°C = 10 + 273.15 = 283.15 K
- Initial pressure (P1) = 50.0 atm
- Gas density (d) = 0.215 g/mL
3. Convert the gas density to moles per liter:
- Molecular weight of CH2 = (12.01 * 2) + (1.008 * 2) = 26.03 g/mol
- 0.215 g/mL (density) = 0.215 g/mL * 1 mL/0.001 L * 1 mol/26.03 g ≈ 0.00826 mol/L
4. Apply the van der Waals equation:
P1 + a(n/V1)^2 = (nRT1)/(V1 - nb)
In this equation:
- P1 is the initial pressure
- a and b are the van der Waals constants (for CH4, a = 2.31 L^2 atm/mol^2 and b = 0.0431 L/mol)
- n is the number of moles, n ≈ 0.00826 mol
- V1 is the initial volume
- R is the ideal gas constant (0.0821 L·atm/(mol·K))
- T1 is the initial temperature
5. We need to find the initial volume, V1. Given the gas density, we can calculate it using the formula:
V1 = n/d
V1 = 0.00826 mol / 0.215 mol/L ≈ 0.038 L
6. Substitute the values into the van der Waals equation:
50.0 atm + (2.31 L^2 atm/(mol^2)) * (0.00826 mol/0.038 L)^2 = (0.00826 mol * 0.0821 L·atm/(mol·K) * 283.15 K) / (0.038 L - (0.0431 L/mol) * 0.00826 mol)
7. Solve the equation for the final pressure P2:
P2 = 50.0 atm + (2.31 L^2 atm/(mol^2)) * (0.00826 mol/0.038 L)^2 - (0.00826 mol * 0.0821 L·atm/(mol·K) * 283.15 K) / (0.038 L - (0.0431 L/mol) * 0.00826 mol)
Finally, calculate the value of P2 using the given equation.
Please note that the answer obtained may be an approximation due to rounding off calculations.