During the combustion of 5.00 g of octane, C8H18, 239.5 kcal (1002 kJ) is released.

Balanced equation: 2C8H18+25O2→16CO2+18H2O

1)How many kilocalories are released by the combustion of 17.7 g of C8H18 ?

2)How many moles of octane must be burned to release 540.0 kcal ?

3)How much energy (in kJ) is released by the combustion of 1.77 mol of C8H18?

During the combustion of 5.00 g of octane, C8H18, 239.5 kcal (1002 kJ) is released.

1. So 5.00 g releases 239.5 kcal, how much is released by 17.7 g? Just convert. Two ways to do this.
239.5 kcal x (17.7 g/5.00g) = ? kcal or set up a proportion like this.
(239.5 kcal/5.00g) = (x kcal/17.7 g) and solve for x.
2. How many moles C8H18 in 5.00 g? That's mols = g/molar mass = 5.00/114 = 0.0438. Now it's done the same reasoning OR proportion as #1.
0.0438 moles releases 239.5 kcal so how many moles (x that is) will it take to release 540.0 kcal?
3. Same reasoning or proportion.
0.0438 mols C8H18 releases 1,002 kJ so how many kJ is released burning 1.77 moles?
I shall be happy to check your work if you post it.

1) Well, if 5.00 g of octane releases 239.5 kcal, then we can use that ratio to find out how many kilocalories are released by 17.7 g of octane. Let's do some math.

239.5 kcal / 5.00 g = x kcal / 17.7 g

Cross multiplying, we get:

(239.5 kcal)(17.7 g) = (5.00 g)(x kcal)

x ≈ 1007.3 kcal

So, approximately 1007.3 kilocalories are released by the combustion of 17.7 g of octane.

2) Now, if 5.00 g of octane releases 239.5 kcal, we can use that ratio to find out how many moles of octane are needed to release 540.0 kcal. Let's get jiggy with some calculations.

239.5 kcal / 5.00 g = 540.0 kcal / y g

Cross multiplying, we get:

(239.5 kcal)(y g) = (5.00 g)(540.0 kcal)

y ≈ 11.3 g

So, approximately 11.3 grams of octane must be burned to release 540.0 kcal.

3) If 1 mole of octane releases 239.5 kcal, then we can use that ratio to find out how much energy is released by the combustion of 1.77 mol of octane. Let's crunch the numbers.

239.5 kcal / 1 mol = x kcal / 1.77 mol

Cross multiplying, we get:

(239.5 kcal)(1.77 mol) = (1 mol)(x kcal)

x ≈ 424.4 kcal

Therefore, approximately 424.4 kilocalories are released by the combustion of 1.77 mol of octane.

To solve these questions, we will use the given balanced equation: 2C8H18 + 25O2 → 16CO2 + 18H2O.

1) To find the number of kilocalories released by the combustion of 17.7 g of C8H18, we need to set up a proportion using the given information:

5.00 g of C8H18 releases 239.5 kcal
17.7 g of C8H18 releases X kcal

Using the proportion, we can solve for X:

5.00 g / 239.5 kcal = 17.7 g / X kcal

Cross multiplying, we get:
5.00 g * X kcal = 239.5 kcal * 17.7 g

X = (239.5 kcal * 17.7 g) / 5.00 g
X ≈ 851.85 kcal

Therefore, approximately 851.85 kilocalories are released by the combustion of 17.7 g of C8H18.

2) To find the number of moles of octane (C8H18) that must be burned to release 540.0 kcal, we will set up a proportion as follows:

5.00 g of C8H18 releases 239.5 kcal
X g of C8H18 releases 540.0 kcal

Using the proportion, we get:
5.00 g / 239.5 kcal = X g / 540.0 kcal

Cross multiplying, we have:
5.00 g * 540.0 kcal = X g * 239.5 kcal

X = (5.00 g * 540.0 kcal) / 239.5 kcal
X ≈ 11.24 g

Therefore, approximately 11.24 grams of octane (C8H18) must be burned to release 540.0 kcal.

3) To find the amount of energy released by the combustion of 1.77 mol of C8H18, we will use the molar mass of C8H18 to convert moles to grams and then use the energy released per gram.

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

Mass of 1.77 mol of C8H18 = 1.77 mol * 114.23 g/mol ≈ 202.14 g

The energy released for 5.00 g of C8H18 is 239.5 kcal.

Using a proportion again:
5.00 g of C8H18 releases 239.5 kcal
202.14 g of C8H18 releases X kcal

X = (5.00 g * 202.14 g) / 239.5 kcal
X ≈ 4.24 kcal

To convert kcal to kJ, we multiply by 4.184 (since 1 kcal = 4.184 kJ):

4.24 kcal * 4.184 kJ/kcal ≈ 17.73 kJ

Therefore, approximately 17.73 kJ of energy is released by the combustion of 1.77 mol of C8H18.

To find the answers to these questions, we need to use the balanced equation provided and perform some calculations based on the given information.

Let's start with the first question:

1) How many kilocalories are released by the combustion of 17.7 g of C8H18?

To find the amount of kilocalories released, we need to determine the amount of octane consumed in the combustion reaction. Here's how you can do it:

Step 1: Calculate the moles of C8H18 using the molar mass.
Molar mass of C8H18 = (12.01 x 8) + (1.01 x 18) = 114.23 g/mol
Moles of C8H18 = mass / molar mass = 17.7 g / 114.23 g/mol = 0.155 mol

Step 2: Use the stoichiometric coefficients from the balanced equation to convert moles of C8H18 to moles of energy released.
From the balanced equation, we see that 2 moles of C8H18 produce 239.5 kcal.
So, 0.155 mol of C8H18 will produce (0.155 mol / 2 mol) * 239.5 kcal = 18.74 kcal.

Therefore, the combustion of 17.7 g of C8H18 would release approximately 18.74 kilocalories.

Moving on to the second question:

2) How many moles of octane must be burned to release 540.0 kcal?

To find the number of moles required, we can use the equation derived from the stoichiometric coefficients:

Moles of C8H18 = (kcal of energy required / kcal per 2 moles of C8H18) * (2 moles / kcal ratio)

From the balanced equation, we can see that 2 moles of C8H18 release 239.5 kcal. Therefore, the kcal ratio is 239.5 kcal / 2 moles.

Plugging in the values:
Moles of C8H18 = (540.0 kcal / 239.5 kcal) * (2 moles / 1 kcal) = 2.25 moles

Thus, to release 540.0 kcal, 2.25 moles of octane must be burned.

Now let's move on to the third question:

3) How much energy (in kJ) is released by the combustion of 1.77 mol of C8H18?

Using the stoichiometric coefficients from the balanced equation, we know that 2 moles of C8H18 release 1002 kJ of energy.

Therefore, the energy released by the combustion of 1.77 mol of C8H18 would be:
Energy = (1.77 mol / 2 mol) * 1002 kJ = 886.21 kJ

Hence, the combustion of 1.77 mol of C8H18 would release approximately 886.21 kJ of energy.