Suppose that coal of density 1.5g/cm3 is pure carbon. The combustion of carbon is described by the equation
C+O2---> CO2 ∆H◦ = −394 kJ
What is the value of q (heat) a ump of coal the size of 7.5cm*7cm*6.5cm is burned? answer in kJ
what mass of water can be heated from 25C to 100C by burning this piece of coal? Answer in grams
volume coal = 7.5*7*6.5 = aprox 340 cc
mass = volume x density = approx 500g but you should recalculate this number and all of the others that follow because I've estimated all of them.
?kJ = apprx 394 kJ x (500/12) = ? and it is exothermic so it has a - sign.
Then
+q = [mass H2O x specific heat H2O x
(Tfinal-Tinitial)]
Substitute and solve for mass H2O
What is the specific heat? And tfinal and tinitial?
The specific heat of H2O should be listed in your text but I think it is 4.184 J/g*c.
Tfinal is listed in the problem as 100 C.
Tinitial is listed in the problem as 25 C.
Note that if you use specific heat in J/g*c you must change q from the first part of the problem from kJ to J and substitute J in the second part of the problem to solve for mass H2O. I ran through the problem quickly and the answer is in the vicinity of 50 g H2O for the second part and about -17 kJ for the first part. Remember to change the sign to + for the second part.
To find the value of q (heat) released when a lump of coal is burned, we need to calculate the amount of energy released from the combustion of carbon.
First, let's calculate the volume of the lump of coal:
Volume = length * width * height
Volume = 7.5 cm * 7 cm * 6.5 cm
Volume = 341.25 cm^3
Next, we need to calculate the mass of the lump of coal:
Density = mass / volume
mass = Density * volume
mass = 1.5 g/cm^3 * 341.25 cm^3
mass = 511.875 g
Now, we can calculate the heat released (q) using the heat of combustion of carbon:
q = mass * ∆H°
q = 511.875 g * (-394 kJ)
q = -201,855 kJ
So, the value of q (heat) released when the lump of coal is burned is -201,855 kJ (negative sign indicates heat release).
Next, let's calculate the mass of water that can be heated from 25°C to 100°C by burning this piece of coal.
We need to use the equation:
q = mc∆T
Where:
q = heat transferred (in kJ)
m = mass of water (in grams)
c = specific heat capacity of water (4.18 J/g°C)
∆T = change in temperature (100°C - 25°C = 75°C)
We know that 1 kJ = 1000 J, so we need to convert q from kJ to J:
q = -201,855 kJ * 1000 J/kJ
q = -201,855,000 J
Now, we can calculate the mass of water:
-201,855,000 J = m * 4.18 J/g°C * 75°C
Divide both sides of the equation by (4.18 J/g°C * 75°C):
m = -201,855,000 J / (4.18 J/g°C * 75°C)
m ≈ -608.076 g
The negative sign indicates that the water would lose mass, which does not make physical sense. Hence, there is an error in the calculation. Please check the values you have provided or the equations used.