Question

a carbohydrate contains c, h, and o. a 10.00 g sample of the compound burns in excess oxygen, forming 27.462 g co₂ and 11.242 g h₂o. how many moles of carbon are in the sample? ? mol c do not round! include lots of digits in your answer since this is part of a larger calculation.

Explanation:

Step1: Find moles of \( CO_2 \)

Molar mass of \( CO_2 \) is \( 12.01 + 2\times16.00 = 44.01 \, g/mol \). Moles of \( CO_2 = \frac{mass}{molar\ mass} = \frac{27.462}{44.01} \).
\[ \frac{27.462}{44.01} = 0.6240 \, (approx, \text{exact calculation: } 27.462\div44.01 = 0.6240) \]

Step2: Moles of C from \( CO_2 \)

In \( CO_2 \), 1 mole of \( CO_2 \) has 1 mole of C. So moles of C = moles of \( CO_2 \).
\[ \text{Moles of C} = \frac{27.462}{44.01} = 0.6240 \, (exact: 27.462\div44.01 = 0.6240) \] (Wait, let's calculate precisely: 27.462 ÷ 44.01. Let's do 27.462 ÷ 44.01: 44.01 × 0.624 = 44.01×0.6 + 44.01×0.024 = 26.406 + 1.05624 = 27.46224, which is very close to 27.462. So 27.462 ÷ 44.01 = 0.624 (exactly, but let's do it as 27.462 / 44.01 = 0.6240 (more precisely, 27.462 ÷ 44.01 = 0.62400... Wait, 44.01 × 0.624 = 27.46224, so 27.462 ÷ 44.01 = 0.624 - (0.00024/44.01) ≈ 0.6239945... So precise value: 27.462 ÷ 44.01 = 0.6239945467... )

Wait, let's do the division properly: 27.462 ÷ 44.01. Let's write it as 27462 ÷ 44010 (multiply numerator and denominator by 1000). Divide numerator and denominator by 6: 4577 ÷ 7335. Let's do long division: 7335 × 0.6 = 4401, 4577 - 4401 = 176. Bring down a zero: 1760. 7335 × 0.02 = 146.7, 1760 - 1467 = 293. Bring down a zero: 2930. 7335 × 0.004 = 29.34, 2930 - 2934 is negative, so 0.003. 7335 × 0.003 = 22.005, 2930 - 2200.5 = 729.5. Bring down a zero: 7295. 7335 × 0.0009 = 6.6015, 7295 - 6601.5 = 693.5. Wait, maybe better to use calculator steps: 27.462 ÷ 44.01. Let's compute 27.462 ÷ 44.01:

44.01 × 0.6 = 26.406

27.462 - 26.406 = 1.056

1.056 ÷ 44.01 = 0.024

So total is 0.6 + 0.024 = 0.624. Wait, because 44.01 × 0.624 = 44.01×0.6 + 44.01×0.02 + 44.01×0.004 = 26.406 + 0.8802 + 0.17604 = 26.406 + 1.05624 = 27.46224, which is 0.00024 more than 27.462. So 27.462 ÷ 44.01 = 0.624 - (0.00024/44.01) = 0.624 - 0.000005453 = 0.623994547. So approximately 0.6239945 mol.

Answer:

0.6239945 (or more precisely, 27.462 / 44.01 = 0.6239945467...)