what volume of benzene ( C6H6 d=0.88g/ml molar mass = 78.11) is required to produce 1.5*10^3 kj of heat
Use the molar heat of reaction, which you will need to look up (or calculate from Heats of formation) , to get the number of moles of C6H6 required. Then convert that to volume using the density and molar mass provided.
This reference has a heat of combustion for C6H6:
http://en.wikipedia.org/wiki/Heat_of_combustion
To determine the volume of benzene required to produce a specific amount of heat, we need to use the equation:
q = m × C × ΔT
Where:
q = heat (in joules or kilojoules)
m = mass of the substance (in grams)
C = specific heat capacity of the substance (in J/g·°C or kJ/kg·°C)
ΔT = change in temperature (in °C)
To solve for the mass of benzene, we'll rearrange the equation and calculate the mass first. Then we can convert it to volume using the known density of benzene.
Step 1: Calculate the mass of benzene.
The given information is the amount of heat (q = 1.5 × 10^3 kJ) and the molar mass (M = 78.11 g/mol; note that this value is unnecessary for this calculation, but it may be useful later).
We know that 1 kJ is equal to 1000 J, so we can convert the heat energy to joules:
q = 1.5 × 10^3 kJ × 1000 J/kJ = 1.5 × 10^6 J
Assuming no temperature change (ΔT = 0°C), we can simplify the equation to:
q = m × C
Rearranging the equation, we get:
m = q / C
Now we need to find the specific heat capacity (C) of benzene. Let's assume it is 1.74 J/g·°C.
Step 2: Calculate the mass of benzene.
m = q / C = 1.5 × 10^6 J / 1.74 J/g·°C
m ≈ 863,013.7 g
Step 3: Calculate the volume of benzene.
We are given the density (d) of benzene, which is 0.88 g/mL. Density is mass (m) divided by volume (V):
d = m / V
Rearranging the equation, we get:
V = m / d
V = 863,013.7 g / 0.88 g/mL
V ≈ 981,162.1 mL
Therefore, the volume of benzene required to produce 1.5 × 10^3 kJ of heat is approximately 981,162.1 mL.