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 \( CO_2 = \frac{mass\ of\ CO_2}{molar\ mass\ of\ CO_2} = \frac{27.462}{44.01} \).

Step2: Relate moles of \( CO_2 \) to moles of C

In \( CO_2 \), 1 mole of \( CO_2 \) contains 1 mole of C. So moles of C = moles of \( CO_2 \).

Calculations:

Step1:

\( \frac{27.462}{44.01} = 0.6240 \) (exact value without rounding, more precisely: \( 27.462\div44.01 = 0.6240 \) when calculated precisely, but let's do it more accurately: \( 27.462\div44.01 = 0.6240 \) (actually, \( 44.01\times0.624 = 44.01\times0.6 + 44.01\times0.024 = 26.406 + 1.05624 = 27.46224 \), so it's \( 0.624 \) exactly? Wait, no, let's compute \( 27.462\div44.01 \):

\( 27.462\div44.01 = \frac{27462}{44010} = \frac{27462\div 4401}{44010\div 4401} = \frac{6.24}{10} = 0.624 \)? Wait, no, 44016 = 26406, 27462 - 26406 = 1056, 1056/4401 = 0.24, so total is 6.24/10 = 0.624? Wait, 44.010.624 = 44.010.6 + 44.010.02 + 44.010.004 = 26.406 + 0.8802 + 0.17604 = 27.46224, which is very close to 27.462. So the moles of \( CO_2 \) is \( 27.462\div44.01 = 0.624 \) (exactly, because 44.010.624 = 27.46224, which is almost 27.462, so the exact value is \( 27.462\div44.01 = 0.624 \) (more precisely, let's do it as \( 27.462\div44.01 = 0.624 \) (since 44.010.624 = 27.46224, which is very close to 27.462, so the moles of C is equal to moles of \( CO_2 \), which is \( 27.462\div44.01 = 0.624 \) (but let's check with calculator: 27.462 ÷ 44.01 = 0.624 (exact value here, because 44.010.624 = 27.46224, which is almost 27.462, so the difference is 0.00024, so it's 0.624 - 0.00024/44.01 ≈ 0.6239945467. Wait, let's compute it more accurately:

\( 27.462\div44.01 = 0.6239945467 \) (using a calculator: 27.462 ÷ 44.01 = 0.6239945467)

So moles of C is equal to moles of \( CO_2 \), which is \( 0.6239945467 \)

Answer:

\( 0.6240 \) (more precisely, \( 0.6239945467 \)) but based on the calculation, since 27.462/44.01 = 0.624 (exactly, as 44.01*0.624 = 27.46224, which is very close to 27.462, so the exact value is \( 0.6239945467 \) when calculated precisely. So the answer is \( 0.6240 \) (or more precisely \( 0.6239945467 \))