I don't know that was important, so I burned it

Chemistry Level 2

There is 7.5 g of an unknown compound which contains only C \ce{C} , H \ce{H} and O . \ce{O}. Before Brilli the scientist could analyze what it is, Harry burned it. Fortunately, the smart scientist collected all the products, which were 11 grams of carbon dioxide and 4.5 grams of water. He then concluded that the empirical formula of the unknown compound is C x H y O z . \text{C}_x\text{H}_y\text{O}_z. What is the value of x + y + z x+y+z ?


The answer is 4.

Christopher Boo by Christopher Boo , 24, Singapore

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2 solutions

Phong Nguyen
May 1, 2014

m O 2 = m C O 2 + m H 2 O − m C x H y O z = 11 + 4.5 − 7.5 = 8 g ⇒ n O = 0.5 m o l n C O 2 = 0.25 m o l ⇒ n C = 0.25 m o l , n O = 0.5 m o l n H 2 O = 0.25 m o l ⇒ n H = 0.5 m o l , n O = 0.25 m o l ⇒ I n 7.5 g o f C x H y O z , n C = 0.25 m o l , n H = 0.5 m o l , n O = 0.25 + 0.5 − 0.5 = 0.25 m o l n C : n H : n O = 0.25 : 0.5 : 0.25 = 1 : 2 : 1 → T h e e m p i r i c a l f o r m u l a o f t h e c o m p o u n d i s C H 2 O , s o x + y + z = 1 + 2 + 1 = 4 m_{O_{2}}=m_{CO_{2}}+m_{H_{2}O}-m_{C_{x}H_{y}O{z}}=11+4.5-7.5=8g \\ \Rightarrow n_O=0.5mol\\ n_{CO_{2}}=0.25mol \Rightarrow n_C=0.25mol,\ n_O=0.5mol \\ n_{H_2O}=0.25mol \Rightarrow n_H=0.5mol,\ n_O=0.25mol \\ \Rightarrow In\ 7.5g\ of\ C_xH_yO_z,\ n_C=0.25mol,\ n_H=0.5mol,\ n_O=0.25+0.5-0.5=0.25mol\\ n_C:n_H:n_O=0.25:0.5:0.25=1:2:1\\ \rightarrow The\ empirical\ formula\ of\ the\ compound\ is\ CH_2O,\ so\ x+y+z=1+2+1=\boxed{4}

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Perfect, but, just to nitpick:

According to a strong convention, using italicized units is bad.

Use mol \text{mol} = \{\text{mol}\} rather than m o l mol .

Bernardo Sulzbach - 6 years, 11 months ago
Royette Posadas
Apr 30, 2014

CO2= 11g and water=4.5g

CxHyOz is 7.5g and therefore O2 is 8g (recall law of conservation of mass)

Calculate the amount( moles) using the molecular mass of the three compounds except the unknown. Again, use the law of conservation of mass to determine the amount(mole) of the unknown which is 0.25 mole. The quotient of 7.5 g/0.25 moles corresponds to 30 g/mol which is the molecular mass of the unknown. Then 12x + y + 16z = 30 (the coeffecients 12, 1, &16 are the amu of C, H, O respectively) and the result is x= 1, y=2, and z=1. The sum is 4.

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