Question

1. aspartame is an artificial sweetener that is 160 times sweeter than sucrose (table sugar) when dissolved in water. it is marketed by g.d. searle as nutra sweet. the molecular formula of aspartame is $c_{14}h_{18}n_{2}o_{5}$. a) calculate the molar mass of aspartame. b) how many moles are in 10.5 g of aspartame? c) how many molecules are in 10.5 g of aspartame?

Explanation:

Step1: Calculate molar mass of aspartame

Molar mass of \(C = 12.01\ g/mol\), \(H=1.008\ g/mol\), \(N = 14.01\ g/mol\), \(O=16.00\ g/mol\)
For \(C_{14}H_{18}N_{2}O_{5}\):

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Step2: Calculate moles of aspartame in \(10.5\ g\)

Use formula \(n=\frac{m}{M}\), where \(m = 10.5\ g\) and \(M = 294.304\ g/mol\)

$$n=\frac{10.5}{294.304}\approx0.0357\ mol$$

Step3: Calculate number of molecules

Use formula \(N=n\times N_{A}\), where \(N_{A}=6.022\times 10^{23}\ mol^{-1}\) and \(n = 0.0357\ mol\)

$$N=0.0357\times6.022\times 10^{23}\approx2.15\times 10^{22}$$

Answer:

a) \(294.304\ g/mol\)
b) \(0.0357\ mol\)
c) \(2.15\times 10^{22}\)