Question

06 question (3 points) open ebook section 2.6 the common pain relievers - aspirin (c9h8o4), acetaminophen (c8h9no2), and naproxen sodium (c14h13o3na) - are available in tablets containing 125 mg of the active ingredient. express your answers to three significant figures. 1st attempt part 1 (1 point) see periodic table 125 mg aspirin = c9h8o4 molecules part 2 (1 point) 125 mg acetaminophen = c8h9no2 molecules part 3 (1 point) 125 mg naproxen sodium = c14h13o3na molecules

Explanation:

Step1: Calculate molar mass

• For aspirin (\(C_9H_8O_4\)):
• Molar mass \(M=(9\times12.01 + 8\times1.008+4\times16.00)\space g/mol\)
• \(M=(108.09+8.064 + 64.00)\space g/mol=180.154\space g/mol\)
• For acetaminophen (\(C_8H_9NO_2\)):
• Molar mass \(M=(8\times12.01+9\times1.008 + 14.01+2\times16.00)\space g/mol\)
• \(M=(96.08+9.072+14.01 + 32.00)\space g/mol = 151.162\space g/mol\)
• For naproxen sodium (\(C_{14}H_{13}O_3Na\)):
• Molar mass \(M=(14\times12.01+13\times1.008+3\times16.00 + 22.99)\space g/mol\)
• \(M=(168.14+13.104+48.00+22.99)\space g/mol=252.234\space g/mol\)

Step2: Convert mass to moles

• Given mass \(m = 125\space mg=0.125\space g\)
• Moles \(n=\frac{m}{M}\)
• For aspirin: \(n=\frac{0.125\space g}{180.154\space g/mol}\approx6.94\times10^{-4}\space mol\)
• For acetaminophen: \(n=\frac{0.125\space g}{151.162\space g/mol}\approx8.27\times10^{-4}\space mol\)
• For naproxen sodium: \(n=\frac{0.125\space g}{252.234\space g/mol}\approx4.95\times10^{-4}\space mol\)

Step3: Calculate number of molecules

• Number of molecules \(N=n\times N_A\) (\(N_A = 6.022\times10^{23}\space mol^{-1}\))
• For aspirin: \(N=6.94\times10^{-4}\space mol\times6.022\times10^{23}\space mol^{-1}\approx4.18\times10^{20}\)
• For acetaminophen: \(N=8.27\times10^{-4}\space mol\times6.022\times10^{23}\space mol^{-1}\approx4.98\times10^{20}\)
• For naproxen sodium: \(N=4.95\times10^{-4}\space mol\times6.022\times10^{23}\space mol^{-1}\approx2.98\times10^{20}\)

Answer:

1. \(4.18\times10^{20}\)
2. \(4.98\times10^{20}\)
3. \(2.98\times10^{20}\)