An electrical heater is used to add 20.50 kJ of heat to a constant-volume calorimeter. The temperature of the calorimeter increases by 5.42°C. When 1.25 g of methanol (CH3OH) is burned in the same calorimeter, the temperature increases by 7.49°C. Calculate the molar heat of combustion for methanol (enter in kJ).
Well, aren't you fired up about this question? Let's heat things up in our calculations!
First, let's calculate the heat capacity of the calorimeter. We can use the formula:
q = m * C * ΔT
Where q is the heat, m is the mass, C is the heat capacity, and ΔT is the change in temperature.
For the electrical heater:
q1 = 20.50 kJ
ΔT1 = 5.42°C
For the calorimeter and methanol:
q2 = q1 = 20.50 kJ (since the heat comes from the same source)
m2 = 1.25 g
ΔT2 = 7.49°C
Now, let's calculate the heat capacity of the calorimeter:
q1 = m1 * C * ΔT1
C = q1 / (m1 * ΔT1)
C = 20.50 kJ / (1 * 5.42°C)
C = 3.779 kJ/°C
Great! Now that we have the heat capacity, we can calculate the molar heat of combustion using the equation:
ΔH = q2 / moles of methanol
To find the moles of methanol, we need to convert grams of methanol to moles using the molar mass. The molar mass of methanol (CH3OH) is 32.04 g/mol.
moles of CH3OH = m2 / molar mass = 1.25 g / 32.04 g/mol
Now, let's calculate the molar heat of combustion:
ΔH = q2 / moles of CH3OH
ΔH = 20.50 kJ / (1.25 g / 32.04 g/mol)
Finally, we calculate the value:
ΔH = 524.64 kJ/mol
So, the molar heat of combustion for methanol is 524.64 kJ/mol. Keep this combustion going and stay hot, my friend!
To calculate the molar heat of combustion for methanol, we need to determine the heat released by the combustion of 1.25 g of methanol and the number of moles of methanol burned.
First, let's calculate the heat released by the combustion of 1.25 g of methanol. We can use the equation:
Q = m * c * ΔT
where:
Q is the heat released
m is the mass of the substance (in this case, methanol)
c is the specific heat capacity of water (which is approximately 4.18 J/g·°C)
ΔT is the change in temperature of the calorimeter
Given that the temperature increase is 7.49°C, the mass of methanol is 1.25 g, and the specific heat capacity of water is 4.18 J/g·°C, we can calculate Q:
Q = (1.25 g) * (4.18 J/g·°C) * (7.49°C)
Q = 39.10 J
Next, we need to convert the heat released (Q) to kilojoules (kJ). Since 1 kJ = 1000 J:
Q = 39.10 J / 1000
Q = 0.0391 kJ
Now, let's determine the number of moles of methanol burned. We can use the equation:
n = m / M
where:
n is the number of moles
m is the mass of the substance (methanol)
M is the molar mass of methanol
The molar mass of methanol (CH3OH) is:
1(12.01 g/mol) + 4(1.01 g/mol) + 16.00 g/mol = 32.04 g/mol
Plugging in the values:
n = (1.25 g) / (32.04 g/mol)
n = 0.039 moles
Finally, we can calculate the molar heat of combustion (ΔH) using the equation:
ΔH = Q / n
ΔH = (0.0391 kJ) / 0.039 moles
ΔH = 1.00 kJ/mole
Therefore, the molar heat of combustion for methanol is 1.00 kJ/mole.
To calculate the molar heat of combustion for methanol, we need to make use of the heat transfer equation and the heat capacity of the calorimeter.
The heat transfer equation is given by:
q = m × c × ΔT
Where:
q is the heat transferred (in joules)
m is the mass of the substance (in grams)
c is the specific heat capacity of the substance (in J/g°C)
ΔT is the change in temperature (in °C)
In this case, we have the heat transfer values and temperature changes for both the electrical heater and the combustion of methanol. We can set up two equations and solve for the specific heat capacity of the calorimeter.
For the electrical heater:
q1 = m1 × c × ΔT1
q1 = 20.50 kJ = 20,500 J (converted to joules)
m1 = mass of the substance (unknown)
c = specific heat capacity of the calorimeter (unknown)
ΔT1 = 5.42°C
For the combustion of methanol:
q2 = m2 × c × ΔT2
q2 = unknown
m2 = 1.25 g
c = specific heat capacity of the calorimeter (from the first equation)
ΔT2 = 7.49°C
Now, let's solve for the specific heat capacity of the calorimeter:
First, calculate the specific heat capacity (c) of the calorimeter using the electrical heater equation:
c = q1 / (m1 × ΔT1)
c = 20,500 J / (m1 × 5.42°C)
Next, substitute the value of c into the combustion equation:
q2 = (1.25 g) × c × (7.49°C)
Now, solve for q2, the heat transferred during the combustion of methanol.
Finally, use the heat transferred during the combustion (q2) to calculate the molar heat of combustion for methanol.
Molar heat of combustion = q2 / (moles of methanol burned)
To determine the number of moles of methanol burned, we need the molar mass of methanol (CH3OH) and the mass of methanol burned.
Molar mass of CH3OH = 32.04 g/mol
moles of methanol burned = mass of methanol burned / molar mass of CH3OH
Substitute the calculated moles of methanol burned into the equation for molar heat of combustion to get the final result.
The first 5.42 degrees C is due to the calorimeter. Total heat for 7.49 C is
20.50 kJ x (7.49/5.42) = 28.329 kJ for combustion CH3OH in that calorimeter.
The difference is about 7.8 kJ but you can do that more accurately. Then 7.8 kJ x (32/1.25) = ? kJ/mol
Check my work.