The combustion of 0.0222g of isooctane vapor, C8H18(g), at constant pressure raises the temperature of a calorimeter 0.400 C. The heat capacity of the calorimeter and water combined is 2.48 kJ/C. Find the molar heat of combustion of gasdeous isooctane.

C8H18(g)+12 1/2O2(g) to 8CO2(g)+9H2O(l)
b. How many grams of C8H18(g) must be burned to obtain 495kJ of heat energy?

q = 2.48 kJ/C x 0.4C = ?? kJ.

??kJ/0.222 = ?kJ/g and
?kJ/g x (1 mole/molar mass) = kJ/mole.

51.10x10^3 kj/mol

To find the molar heat of combustion of gaseous isooctane, we can use the equation:

C8H18(g) + 12.5O2(g) → 8CO2(g) + 9H2O(l)

First, we need to calculate the heat produced by the combustion of 0.0222g of isooctane. We can use the equation:

q = m * C * ΔT

where:
q = heat produced
m = mass of isooctane (0.0222g)
C = heat capacity of the calorimeter and water combined (2.48 kJ/°C)
ΔT = change in temperature (0.400°C)

Plugging in the values:

q = 0.0222g * 2.48 kJ/°C * 0.400°C
q = 0.0222g * 2.48 kJ
q ≈ 0.055kg * 2.48 kJ
q ≈ 0.1364 kJ

Next, we need to convert the heat produced to the molar heat of combustion. Since the combustion of 0.0222g of isooctane produces 0.1364 kJ of heat, we can calculate the molar heat of combustion using the stoichiometry of the balanced equation:

0.0222g of isooctane ↔ 0.1364 kJ

To find the molar heat of combustion per mole of isooctane, we need to convert grams to moles. The molar mass of isooctane (C8H18) is:

Molar mass of C = 12.01 g/mol
Molar mass of H = 1.01 g/mol
Therefore, molar mass of C8H18 = (12.01 g/mol * 8) + (1.01 g/mol * 18) = 114.23 g/mol

Converting grams to moles:

0.0222g / 114.23 g/mol = 0.000194 moles

Now we can calculate the molar heat of combustion:

0.000194 moles of isooctane ↔ 0.1364 kJ

To find the molar heat of combustion per mole of isooctane, we divide 0.1364 kJ by 0.000194 moles:

Molar heat of combustion = 0.1364 kJ / 0.000194 moles
Molar heat of combustion ≈ 704.12 kJ/mol

Therefore, the molar heat of combustion of gaseous isooctane is approximately 704.12 kJ/mol.

b. To find the grams of isooctane required to obtain 495 kJ of heat energy, we can use the molar heat of combustion and stoichiometry of the balanced equation:

0.000194 moles of isooctane ↔ 0.1364 kJ

To find the moles of isooctane required to obtain 495 kJ of heat energy, we can rearrange the equation:

moles of isooctane = (495 kJ * 0.000194 moles) / 0.1364 kJ
moles of isooctane ≈ 0.00704 moles

Converting moles to grams:

grams of isooctane = 0.00704 moles * 114.23 g/mol
grams of isooctane ≈ 0.804 g

Therefore, approximately 0.804 grams of isooctane must be burned to obtain 495 kJ of heat energy.

To find the molar heat of combustion of isooctane (C8H18), we can use the data given to calculate the heat released during the combustion reaction.

1. First, we need to calculate the amount of heat released by the combustion reaction using the formula:

q = m * C * ΔT

where:
q = heat released (in joules)
m = mass of the substance (in grams)
C = heat capacity of the calorimeter and water combined (in J/g·°C)
ΔT = temperature change (in °C)

In this case, we are given the heat capacity of the calorimeter and water combined as 2.48 kJ/°C. To use this value in the formula, we need to convert it to J/g·°C. There are 1000 J in 1 kJ, so 2.48 kJ is equivalent to 2480 J.

Now, we can substitute the given values into the formula:

q = (0.0222 g) * (2480 J/g·°C) * (0.400 °C)

Calculating this, we get:

q = 17.728 J

2. Next, we need to convert the heat released to the molar heat of combustion of isooctane. The molar heat of combustion is defined as the heat released when 1 mole of a substance is burned.

To do this, we need to calculate the number of moles of isooctane burned in the given combustion reaction. From the balanced equation, we can see that 1 mole of C8H18 produces 8 moles of CO2.

The molar heat of combustion can be calculated using the formula:

ΔH = q / n

where:
ΔH = molar heat of combustion (in J/mol)
q = heat released (in J)
n = number of moles of the substance burned (in mol)

From the balanced equation, we know that 1 mole of C8H18 produces 8 moles of CO2. So the number of moles of C8H18 burned would be 1/8 of the number of moles of CO2 produced.

We need to find the number of moles of CO2 produced. To do this, we can use the ideal gas law equation:

PV = nRT

where:
P = pressure (in atm)
V = volume (in L)
n = number of moles
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature (in K)

Given that the combustion is at constant pressure, we can assume the volume and pressure do not change. The number of moles of CO2 produced can be calculated using the equation:

n = PV / RT

Given that we are not provided with the volume, pressure, or temperature, we cannot directly calculate the number of moles of CO2 produced.

Therefore, it is not possible to directly find the molar heat of combustion of isooctane without additional data.

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For the second part of your question, to calculate the mass of isooctane (C8H18) that must be burned to obtain a certain amount of heat energy, we can use the formula:

q = m * C * ΔT

where:
q = heat released (in joules)
m = mass of the substance (in grams)
C = heat capacity of the calorimeter and water combined (in J/g·°C)
ΔT = temperature change (in °C)

In this case, we are given the heat released as 495 kJ. To use this value in the formula, we need to convert it to J. There are 1000 J in 1 kJ, so 495 kJ is equivalent to 495,000 J.

Now, we can rearrange the formula to solve for the mass, m:

m = q / (C * ΔT)

Substituting the given values:

m = (495,000 J) / (2.48 kJ/°C * 0.400 °C)

Calculating this, we get:

m = 496.8 g

Therefore, approximately 497 grams of isooctane must be burned to obtain 495 kJ of heat energy.