a 47.7L sample of a gaseous hydrocarbon, measured at 1.00atm and 25degreesC is burned in excess oxygen, liberating 4.33X10^3 kJ of heat at a constant pressure. what is the identity of the hydrocarbon?
possible answer choices:
A. ethane (C2H6 change in Hf= -84.68kj/mol
B. ethylene (C2H4 change in Hf= 52.47kj/mol
C. acetylene (C2H2 change in Hf= 226.73 kj/mol
D. propane (C3H8 change in Hf= -104.7kj/mol
E. propylene (C3H6 change in Hf=
20.41 kj/mol
To determine the identity of the hydrocarbon, we need to use the information provided about the volume, pressure, temperature, and heat released. Here's how to approach the problem step by step:
1. Let's start by converting the volume from liters to moles using the Ideal Gas Law. The formula is:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles
R = gas constant (0.0821 L·atm/mol·K)
T = temperature (in Kelvin)
Given: V = 47.7 L
P = 1.00 atm
T = 25°C = (25 + 273) K = 298 K
Now we can find the number of moles (n) using the formula:
n = PV / RT
n = (1.00 atm * 47.7 L) / (0.0821 L·atm/mol·K * 298 K)
n ≈ 1.92 mol
2. Next, we need to calculate the amount of heat released during the combustion. The formula for heat (q) is:
q = mcΔT
Where:
q = heat released (in Joules or kJ)
m = mass of the substance (in grams)
c = specific heat capacity
ΔT = change in temperature (in Kelvin)
In this case, since the heat is released at constant pressure, we can use the formula:
q = ΔH
Where:
ΔH = heat of combustion (in kJ)
Given: q = 4.33 × 10^3 kJ
The heat of combustion provides the energy released when one mole of the hydrocarbon is burned completely. Therefore, the heat of combustion is equivalent to the molar heat of combustion.
3. Now, we can calculate the molar heat of combustion (ΔH) using the formula:
ΔH = q / n
ΔH = (4.33 × 10^3 kJ) / 1.92 mol
ΔH ≈ 2.259 kJ/mol
4. Finally, we compare the molar heat of combustion obtained with known values for different hydrocarbons. The hydrocarbon that matches the closest molar heat of combustion is the likely identity.
It's important to note that different hydrocarbon molecules can have different isomers, so further analysis might be required to determine the exact molecular structure of the hydrocarbon.