Question

2kclo₃ = 2kcl + 3o₂
determine how many moles of oxygen gas are produced if the reaction also produced 254 grams of potassium chloride

Explanation:

Step1: Find molar mass of KCl

Molar mass of K (potassium) is 39.10 g/mol, and molar mass of Cl (chlorine) is 35.45 g/mol. So molar mass of KCl is $39.10 + 35.45 = 74.55$ g/mol.

Step2: Calculate moles of KCl

Given mass of KCl is 254 g. Moles of KCl = $\frac{\text{mass}}{\text{molar mass}} = \frac{254}{74.55} \approx 3.41$ mol (rounded to two decimal places).

Step3: Use stoichiometry from reaction

The balanced reaction is $2KClO_3 = 2KCl + 3O_2$. From the reaction, 2 moles of KCl are produced with 3 moles of $O_2$. So the mole ratio of $O_2$ to KCl is $\frac{3}{2}$.

Step4: Calculate moles of $O_2$

Moles of $O_2$ = moles of KCl $\times \frac{3}{2}$ = $3.41 \times \frac{3}{2} = 5.115$ mol (or more precisely, using the exact moles of KCl without rounding early: $\frac{254}{74.55} \times \frac{3}{2} = \frac{254\times3}{74.55\times2} = \frac{762}{149.1} = 5.11$ mol approximately, but let's do it more accurately. Wait, 254 divided by 74.55: 74.553 = 223.65, 254 - 223.65 = 30.35, 30.35/74.55 ≈ 0.407, so total moles of KCl ≈ 3.407. Then moles of $O_2$ = 3.407 3/2 = 5.1105 mol, approximately 5.11 mol. But let's check with exact calculation: 254 / 74.55 = 2540 / 745.5 ≈ 3.407. Then 3.407 * 3/2 = 5.1105, so approximately 5.11 moles. Wait, but maybe we can do it without rounding. Let's see:

Moles of KCl = 254 g / 74.55 g/mol = 254 / 74.55. Let's compute that: 74.55 3 = 223.65, 254 - 223.65 = 30.35. 30.35 / 74.55 = 607 / 1491 ≈ 0.407. So total moles KCl ≈ 3.407. Then moles O2 = (3/2)3.407 = 5.1105 ≈ 5.11 mol. But let's check the exact value:

254 divided by 74.55: 74.55 × 3 = 223.65, 254 - 223.65 = 30.35. 30.35 ÷ 74.55 = 3035 ÷ 7455 = divide numerator and denominator by 5: 607 ÷ 1491 ≈ 0.407. So total moles KCl = 3 + 0.407 = 3.407. Then moles O2 = 3.407 × 3/2 = 5.1105 ≈ 5.11 mol. Alternatively, using more precise calculation:

74.55 g/mol is the molar mass of KCl. So 254 g KCl is 254 / 74.55 = 3.407 mol KCl (exact value: 254 ÷ 74.55 = 3.4070825 mol). Then, from the reaction, 2 moles KCl produce 3 moles O2. So moles O2 = (3/2) moles KCl = (3/2) 3.4070825 = 5.11062375 mol, which is approximately 5.11 moles. But maybe we can do it as:

254 g KCl (1 mol KCl / 74.55 g KCl) (3 mol O2 / 2 mol KCl) = (254 3) / (74.55 2) = 762 / 149.1 = 5.110664... So approximately 5.11 moles. Wait, but let's check the molar mass again. K is 39.10, Cl is 35.45, so 39.10 + 35.45 = 74.55 g/mol, correct. So 254 divided by 74.55: 74.55 3 = 223.65, 254 - 223.65 = 30.35. 30.35 / 74.55 = 0.407, so total 3.407 mol KCl. Then 3.407 3/2 = 5.1105 mol O2. So approximately 5.11 moles. But maybe the answer is expected to be 5.11 or 5.1 or 5. Let's see, maybe we made a mistake in molar mass? Wait, K is 39.0983, Cl is 35.453, so molar mass of KCl is 39.0983 + 35.453 = 74.5513 g/mol. So 254 / 74.5513 ≈ 3.407 mol KCl. Then 3.407 * 3/2 = 5.1105 mol O2. So approximately 5.11 moles. So the answer is approximately 5.11 moles, or more precisely, 5.11 mol.

Answer:

The number of moles of oxygen gas produced is approximately $\boxed{5.11}$ moles (or more precisely, using exact calculation, it's approximately 5.11 moles). Wait, but let's check again. Wait, 254 grams of KCl. Let's do the calculation step by step:

1. Molar mass of KCl: K (39.10 g/mol) + Cl (35.45 g/mol) = 74.55 g/mol.

1. Moles of KCl: 254 g / 74.55 g/mol = 3.407 mol (as above).

1. From the balanced equation: 2 moles KCl → 3 moles O2. So the ratio is 3 moles O2 / 2 moles KCl.

1. Moles of O2: 3.407 mol KCl (3 mol O2 / 2 mol KCl) = 5.1105 mol O2. So approximately 5.11 moles. So the answer is 5.11 moles (or 5.1 moles, or 5 moles depending on significant figures. Wait, 254 grams is three significant figures, molar mass of KCl is 74.55 (four significant figures), so the moles of KCl is 254 / 74.55 = 3.407 (four significant figures), then moles of O2 is 3.407 3/2 = 5.1105, which is approximately 5.11 moles (three significant figures, since 254 has three). So the answer is 5.11 moles.