Question

consider the following decomposition reaction:
2h₂o(g) + 484. kj → 2h₂(g) + o₂(g)
calculate the mass (in grams) of o₂ produced when 1.88×10⁴ kj is consumed in this reaction. report your answer in scientific notation. be sure your answer has the correct number of significant figures.
g o₂

Explanation:

Step1: Find moles of O₂ from energy

From the reaction, 484 kJ produces 1 mol O₂.
Moles of O₂ = $\frac{1.88 \times 10^4\ \text{kJ}}{484\ \text{kJ/mol}}$
Calculate: $\frac{1.88 \times 10^4}{484} \approx 38.84\ \text{mol}$

Step2: Calculate mass of O₂

Molar mass of O₂ is 32.00 g/mol.
Mass = moles × molar mass
Mass = $38.84\ \text{mol} \times 32.00\ \text{g/mol}$
Calculate: $38.84 \times 32.00 \approx 1.243 \times 10^3\ \text{g}$ (adjust sig figs: 1.88 has 3 sig figs, 484 has 3, so result has 3 sig figs)

Wait, correction: Let's redo Step1 with exact calculation.

Step1: Moles of O₂ = $\frac{1.88 \times 10^4\ \text{kJ}}{484\ \text{kJ/mol O}_2}$
$= \frac{1.88 \times 10^4}{484}\ \text{mol O}_2$
$≈ 38.842975\ \text{mol O}_2$

Step2: Mass = $38.842975\ \text{mol} \times 32.00\ \text{g/mol}$ (O₂ molar mass is 32.00 g/mol)
$= 1242.9752\ \text{g}$
In scientific notation, with 3 sig figs: $1.24 \times 10^3$? Wait, no, let's check sig figs again.

Wait, 1.88 × 10⁴ has 3 sig figs, 484 has 3. So the ratio gives 3 sig figs. Then 38.8 (3 sig figs) × 32.00 (4 sig figs) → 3 sig figs. Wait, 38.842975 is ~38.8 (3 sig figs? No, 1.88×10⁴ / 484: 1.88 has 3, 484 has 3, so the result should have 3 sig figs. So 38.8 mol (3 sig figs). Then 38.8 × 32.00 = 1241.6 → 1.24 × 10³? Wait, no, 38.842975 × 32 = 1242.9752, which is 1.24 × 10³ when rounded to 3 sig figs? Wait, 1242.9752 is 1.24 × 10³? No, 1.24 × 10³ is 1240, but 1242.9752 is closer to 1.24 × 10³? Wait, no, 1242.9752 is 1.24 × 10³ (3 sig figs) or 1.243 × 10³? Wait, let's do the calculation more accurately.

Wait, the reaction: 2 H₂O(g) + 484 kJ → 2 H₂(g) + O₂(g). So per 484 kJ, 1 mol O₂ is produced. So moles of O₂ = (1.88×10⁴ kJ) / (484 kJ/mol O₂) = (1.88×10⁴ / 484) mol O₂. Let's compute that:

1.88×10⁴ = 18800
18800 / 484 ≈ 38.8429752 mol O₂

Then mass O₂ = 38.8429752 mol × 32.00 g/mol = 1242.9752 g

Now, convert to scientific notation with 3 sig figs: 1.24 × 10³? Wait, 1242.9752 is 1.24 × 10³? No, 1.24 × 10³ is 1240, but 1242.9752 is 1.24 × 10³ (since the third sig fig is 4, and the next digit is 2, which is less than 5? Wait, no, 1242.9752: the first three digits are 1,2,4. The next digit is 2, so we keep 1.24 × 10³? Wait, no, 1242.9752 is 1.24 × 10³ when rounded to three significant figures? Wait, 1242.9752: the number is 1 2 4 2 . 9 7 5 2. So the first three significant figures are 1,2,4. The next digit is 2, which is less than 5, so we don't round up. So 1.24 × 10³ g. Wait, but let's check the calculation again.

Wait, 1.88×10⁴ kJ / 484 kJ per mol O₂ = (1.88 / 484) × 10⁴ mol O₂. 1.88 / 484 ≈ 0.0038842975. Then 0.0038842975 × 10⁴ = 38.842975 mol O₂. Then 38.842975 mol × 32.00 g/mol = 1242.9744 g. Now, 1242.9744 g in scientific notation with three significant figures: 1.24 × 10³ g? Wait, 1242.9744 is 1.24 × 10³? No, 1.24 × 10³ is 1240, but 1242.9744 is 1.24 × 10³ (since the fourth digit is 2, which is less than 5, so we don't round up the third digit). Wait, but 1242.9744 is 1.24 × 10³ when rounded to three significant figures? Wait, no, 1242.9744: the first three significant figures are 1, 2, 4. The next digit is 2, so we keep it as 1.24 × 10³. Alternatively, maybe I made a mistake in the molar ratio. Wait, the reaction produces 1 mol O₂ per 484 kJ. So yes, moles of O₂ = energy / 484 kJ per mol O₂. Then mass is moles × molar mass.

Wait, let's check the calculation again:

1.88 × 10⁴ kJ ÷ 484 kJ/mol O₂ = (1.88 / 484) × 10⁴ mol O₂
1.88 ÷ 484 = 0.0038842975
0.0038842975 × 10⁴ = 38.842975 mol O₂

38.842975 mol O₂ × 32.00 g/mol O₂ = 1242.9752 g O₂

Now, convert to scientific notation with three significant figures: 1.24 × 10³ g? Wait, 1242.9752 is 1.24 × 10³? No, 1.24 × 10³ is 1240, but 1242.9752 is 1.24 × 10³ (since the third significant figure is 4, and the next digit is 2, which is less than 5, so we don't round up). Alternatively, maybe the answer is 1.24 × 10³ g, but let's check the sig figs again. The given values: 1.88 × 10⁴ (3 sig figs), 484 (3 sig figs), 32.00 (4 sig figs). When multiplying/dividing, the result should have the least number of sig figs, which is 3. So 1242.9752 rounded to 3 sig figs is 1240? Wait, no, 1242.9752: the first three digits are 1, 2, 4. The next digit is 2, so we keep it as 1240? No, 1242.9752 is closer to 1240? No, 1242.9752 is 1243, which is 1.24 × 10³ (since 1.24 × 10³ is 1240, but 1243 is 1.24 × 10³ when rounded to three significant figures? Wait, no, 1243 is 1.24 × 10³ (three sig figs) because the third digit is 4, and the next digit is 3, which is less than 5. Wait, no, 1243: the first three significant figures are 1, 2, 4. The fourth digit is 3, so we don't round up. So 1.24 × 10³ g.

Wait, but let's do the calculation with exact numbers:

Moles of O₂ = (1.88 × 10⁴ kJ) / (484 kJ/mol) = (1.88 / 484) × 10⁴ mol = 0.0038842975 × 10⁴ mol = 38.842975 mol

Mass of O₂ = 38.842975 mol × 32.00 g/mol = 1242.9744 g ≈ 1.24 × 10³ g (with three significant figures)

Answer:

$\boxed{1.24 \times 10^3}$