I am stuck on b)...
Reacting 1 L of H2(g) with 1 L C2H2(g) (both at STP) results in the formation of 1 L of C2H4(g) if the reaction is maintained at the same conditions (STP) and goes to completion. If this reaction produced 6.3 kJ of heat (absorbed by the surroundings), calculate: a) the PV work and b) the heat evolved,c) the change in internal energy of the system, and d) the change in internal energy of the surroundings.
My answers:
a) w= 2.27 x10^3 J Is this correct?
b) Is this set up correct?
Heat evolved:
q=(67,200g)x(4.184J/gC)x(273K)=..
I am not sure what is the temperature change...
c) dE=q+w.. But I need part b) checked before I can do part c) correctly..
d) Would the answer for part d) be the same as part c) but with different sign?
C2H2 + H2 ==> C2H4 + 6.3 kJ
I don't know how you obtained that answer for a.
Isn't be just 6.3 kJ?
As for the T change, the problem states it is STP at the beginning and is maintained at STP.
As for your calculation for b, how did the specific heat H2O get in there.?
Let's go through each part of the question and how to solve it:
a) PV work:
To calculate the PV work, we can use the ideal gas law, which states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin. In this case, both reactants and products are at STP (standard temperature and pressure). The pressure at STP is 1 atm, and the temperature is 273 K.
Since we're given that 1 L of H2 and 1 L of C2H2 react to produce 1 L of C2H4, we can assume that the volume remains constant during the reaction. Therefore, the change in volume is zero (ΔV = 0).
Using the ideal gas law, we can calculate the number of moles of gas in each case:
n(H2) = V(H2) / (RT) = 1 L / (0.0821 L∙atm/(mol∙K) x 273 K) = 0.0436 mol
n(C2H2) = V(C2H2) / (RT) = 1 L / (0.0821 L∙atm/(mol∙K) x 273 K) = 0.0436 mol
n(C2H4) = V(C2H4) / (RT) = 1 L / (0.0821 L∙atm/(mol∙K) x 273 K) = 0.0436 mol
Since the reaction goes to completion, there is a 1:1 molar ratio between H2/C2H2 and C2H4. Therefore, the number of moles of C2H4 formed is also 0.0436 mol.
Since the volume change is zero, the PV work is given by the equation:
w = -PΔV = 0
So, the PV work is zero.
b) Heat evolved:
To calculate the heat evolved, we need to use the equation q = ΔH, where q is the heat and ΔH is the change in enthalpy. In this case, the heat evolved is equal to the heat absorbed by the surroundings.
We're given that the reaction produces 6.3 kJ of heat (absorbed by the surroundings). To convert this value to joules, we multiply it by 1000 (1 kJ = 1000 J):
q = 6.3 kJ * 1000 J/kJ = 6300 J
c) Change in internal energy of the system:
The change in internal energy (ΔE) of the system is equal to the sum of the heat (q) and the work (w) done on or by the system. In this case, since the PV work is zero, the change in internal energy is simply equal to the heat evolved:
ΔE = q = 6300 J
d) Change in internal energy of the surroundings:
The change in internal energy of the surroundings is equal in magnitude but opposite in sign to the change in internal energy of the system. In this case:
ΔE(surroundings) = -ΔE(system) = -6300 J
So, to summarize:
a) The PV work is zero.
b) The heat evolved is 6300 J.
c) The change in internal energy of the system is 6300 J.
d) The change in internal energy of the surroundings is -6300 J.