Calcium oxide and carbon are reacted to produce carbon monoxide and calcium carbide CaC2. When one mole of calcium carbide is formed, 464.8kJ is absorbed.


How many grams of carbon are used up when 20.00kJ of heat is absorbed?

CaO + 3C ==> CO + CaC2

464.8 kJ is produced when 1 mol (64g) CaC2 is formed or 3 mol C (36g) is used.
36g C x (20.00 kJ/464.8 kJ) = ? g C used.

Well, let's do some chemistry math with a touch of comedy!

First, we need to find out how many moles of calcium carbide are formed when 464.8kJ of heat is absorbed. We can use the molar enthalpy to convert kJ to moles.

Now, it's important to note that one mole of calcium carbide forms when 464.8 kJ is absorbed. So, if we divide 20.00 kJ by 464.8 kJ/mol, we'll get the number of moles of calcium carbide formed.

But wait, we're not done yet! We need to find the number of moles of carbon used up in the reaction. From the balanced chemical equation, we know that for every mole of calcium carbide, we need one mole of carbon. So, the number of moles of carbon used up will be the same as the number of moles of calcium carbide.

Finally, we can calculate the mass of carbon used up. We multiply the number of moles by the molar mass of carbon.

So, grab your calculators and let the math begin!

To find the mass of carbon used up when 20.00 kJ of heat is absorbed, we need to use the given information about the heat absorbed when one mole of calcium carbide is formed.

From the information given, we know that when one mole of calcium carbide (CaC2) is formed, 464.8 kJ of heat is absorbed.

Now, we can set up a proportion to relate the amount of heat absorbed to the amount of carbon used up.

Let's call the mass of carbon used up "x" grams.

Since the heat absorbed is directly proportional to the amount of carbon used up, we can set up the proportion:

464.8 kJ / 1 mole = 20.00 kJ / x grams

Now, we need to convert kJ to J by multiplying by 1000:

464.8 kJ = 464,800 J
20.00 kJ = 20,000 J

The proportion becomes:

464,800 J / 1 mole = 20,000 J / x grams

Next, we need to find the molar mass of carbon (C). The molar mass of carbon is approximately 12.01 g/mol.

Now, we can solve the proportion:

464,800 J / 1 mole = 20,000 J / x grams
464,800 J x grams = 20,000 J x 1 mole
464,800 J x grams = 20,000 J
x grams = (20,000 J / 464,800 J) x 1 mole
x grams ≈ 0.04299 moles

Lastly, we can convert moles to grams using the molar mass of carbon:

Mass of carbon = 0.04299 moles x 12.01 g/mol
Mass of carbon ≈ 0.516 g

Therefore, approximately 0.516 grams of carbon are used up when 20.00 kJ of heat is absorbed.

To find the number of grams of carbon used up when a certain amount of heat is absorbed, we need to use the given enthalpy change for the reaction.

Given:
- Enthalpy change for the formation of 1 mole of calcium carbide (CaC2) = 464.8 kJ

First, we need to calculate the number of moles of calcium carbide that corresponds to 20.00 kJ of heat absorbed.

Using the equation:
ΔH = q / n

Where:
- ΔH is the enthalpy change (464.8 kJ)
- q is the heat absorbed (-20.00 kJ, since it is absorbed)
- n is the number of moles of calcium carbide formed

Solving for n:
n = q / ΔH
n = (-20.00 kJ) / (464.8 kJ/mol)
n ≈ -0.04298 mol

Note: The negative sign indicates that heat is absorbed.

Since the balanced chemical equation for the reaction is:
CaO + 3C ⟶ CaC2 + CO

We can see that three moles of carbon react to produce one mole of calcium carbide. Therefore, the number of moles of carbon used up is three times the number of moles of calcium carbide formed.

Number of moles of carbon = 3 * n
Number of moles of carbon ≈ 3 * (-0.04298 mol)
Number of moles of carbon ≈ -0.12894 mol

Again, the negative sign indicates that carbon is being used up.

To find the mass of carbon used up, we need the molar mass of carbon (12.01 g/mol).

Mass of carbon = Number of moles of carbon * Molar mass of carbon
Mass of carbon ≈ -0.12894 mol * (12.01 g/mol)
Mass of carbon ≈ -1.549 g

Since mass cannot be negative, we neglect the negative sign, and the final answer is approximately 1.549 grams of carbon used up.

Therefore, approximately 1.549 grams of carbon are used up when 20.00 kJ of heat is absorbed.