Question

skills check
checkpoint ii
find the molecular formula of an
unknown sugar.
a sugar was discovered in the nineteenth
century that the body metabolizes slowly,
preventing spikes in blood sugar. it has an
e mpirical formula of ( c_3h_7o_3 ) and a molar
mass of 182.17 g/mol. what is the molecular
formula of this sugar?
empirical formula
weight =?
( c_3h_7o_3 )
molecular formula
weight = 182 amu
( c_?h_?o_? )

Explanation:

Step1: Calculate the empirical formula weight

The atomic masses of \(C = 12.01\space g/mol\), \(H= 1.008\space g/mol\), \(O = 16.00\space g/mol\).
For \(C_3H_7O_3\), the empirical formula weight \(M_{empirical}=(3\times12.01)+(7\times1.008)+(3\times16.00)\)
\(M_{empirical}=36.03 + 7.056+48.00=91.086\space g/mol\)

Step2: Find the ratio \(n\)

We know that \(n=\frac{M_{molecular}}{M_{empirical}}\)
Given \(M_{molecular} = 182.17\space g/mol\) and \(M_{empirical}=91.086\space g/mol\)
\(n=\frac{182.17}{91.086}\approx2\)

Step3: Determine the molecular formula

Multiply the sub - scripts in the empirical formula by \(n\).
For \(C_3H_7O_3\), when \(n = 2\), the molecular formula is \(C_{3\times2}H_{7\times2}O_{3\times2}=C_6H_{14}O_6\)

Answer:

\(C_6H_{14}O_6\)