When 3.00 g of butane, C4H10, are combusted in a calorimeter containing 800. g of water, the temperature of the water changes by 44.4 °C. What is the heat of combustion of butane in kilojoules per mole? The molar mass of butane is 58.123 g/mol. The specific heat of water is 4.18 J/g·°C. Please indicate whether the reaction was endothermic or exothermic with the sign of your answer.
Well, well, well! It seems we have to do some chemistry calculations here. Don't worry, I won't make you sweat like that calorimeter. Let's get started!
First, we need to calculate the heat absorbed by the water. The formula for heat (q) is given by:
q = m * c * ΔT
Where:
- m is the mass of water (800 g)
- c is the specific heat of water (4.18 J/g·°C)
- ΔT is the change in temperature (44.4 °C)
Plugging in the values, we get:
q = 800 g * 4.18 J/g·°C * 44.4 °C
Multiplying these numbers gives us:
q = 148131.2 J
Now, we need to convert the joules to kilojoules, because joules are so overrated. One kilojoule (kJ) is equal to 1000 joules. So:
q = 148131.2 J / 1000
q = 148.1312 kJ
Now, to find the heat of combustion of butane (C4H10) per mole, we have to use the molar mass of butane (58.123 g/mol). We know that 3.00 g of butane was combusted, so we can calculate the number of moles (n).
n = mass / molar mass
n = 3.00 g / 58.123 g/mol
n ≈ 0.0516 mol
Finally, we divide the heat absorbed by the number of moles:
Heat of combustion per mole = q / n
Heat of combustion per mole = 148.1312 kJ / 0.0516 mol
Heat of combustion per mole ≈ 2865.28 kJ/mol
And there you have it! The heat of combustion of butane is approximately 2865.28 kilojoules per mole.
As for the sign, since the water's temperature increased, heat was released to the surroundings, so the reaction is exothermic. Therefore, the heat of combustion is negative, indicating heat release.
To find the heat of combustion of butane in kilojoules per mole, we will first calculate the heat released by the combustion of butane, and then convert it to kilojoules per mole.
1. Calculate the heat released by the combustion of butane:
To find the heat released, we can use the equation:
q = msΔT
Where:
- q is the heat released or absorbed (in Joules)
- m is the mass of water (in grams)
- s is the specific heat of water (in J/g·°C)
- ΔT is the change in temperature (in °C)
In this case, m = 800 g, s = 4.18 J/g·°C, and ΔT = 44.4 °C.
q = (800 g) * (4.18 J/g·°C) * (44.4 °C)
q = 148,339.2 J
2. Convert Joules to kilojoules:
To convert Joules to kilojoules, we divide the value by 1000.
q = 148,339.2 J / 1000
q = 148.34 kJ
3. Calculate the number of moles of butane combusted:
To find the number of moles, we can use the equation:
moles = mass / molar mass
In this case, mass = 3.00 g and molar mass = 58.123 g/mol.
moles = 3.00 g / 58.123 g/mol
moles = 0.0517 mol
4. Calculate the heat of combustion per mole of butane:
To find the heat of combustion per mole, we divide the heat released by the number of moles.
heat of combustion per mole = q / moles
heat of combustion per mole = 148.34 kJ / 0.0517 mol
heat of combustion per mole ≈ 2860.11 kJ/mol
The heat of combustion of butane is approximately 2860.11 kJ/mol.
Since the heat is released during the combustion reaction, the reaction is exothermic.
To find the heat of combustion of butane in kilojoules per mole, we will use the formula:
q = mc∆T
Where:
q = heat absorbed or released
m = mass
c = specific heat capacity
∆T = change in temperature
Step 1: Calculate the heat (q) absorbed or released by the water.
q_water = mc_water∆T_water
Given:
m_water = 800 g
c_water = 4.18 J/g·°C
∆T_water = 44.4 °C
q_water = (800 g)(4.18 J/g·°C)(44.4 °C)
q_water = 148243.2 J
Step 2: Convert the heat (q) from joules to kilojoules.
1 kilojoule (kJ) = 1000 joules (J)
q_water_kilojoules = 148243.2 J / 1000
q_water_kilojoules = 148.2432 kJ
Step 3: Calculate the moles of butane burned.
Given:
mass_butane = 3.00 g
molar_mass_butane = 58.123 g/mol
moles_butane = mass_butane / molar_mass_butane
moles_butane = 3.00 g / 58.123 g/mol
moles_butane = 0.0516 mol
Step 4: Calculate the molar heat of combustion.
Molar heat of combustion = q_water_kilojoules / moles_butane
Molar heat of combustion = 148.2432 kJ / 0.0516 mol
Molar heat of combustion = 2870.39 kJ/mol
Therefore, the heat of combustion of butane is 2870.39 kJ/mol.
To determine if the reaction was endothermic or exothermic, we need to consider the sign of the heat release. Since the temperature of the water increased during the combustion of butane, heat was released. Hence, the reaction is exothermic.
q = mass H2O x specific heatH2O x delta T.
Solve for q. Since the temperature rose you know the heat was generated by the combustion of the butane so it was an exothermic reaction. That q is in J/3.00 g. Change to kJ/3.00 g, then
kJ/3.00 g x (molar mass butane) = kJ/mol.