Question

a virus has a mass of ( 9.0\times10^{-12} ) mg and an oil tanker has a mass of ( 3.0\times10^{7} ) kg. use this information to answer the questions below. be sure your answers have the correct number of significant digits. what is the mass of 1 mole of viruses? round your answer to 2 significant digits. how many moles of viruses have a mass equal to the mass of an oil tanker? round your answer to 2 significant digits.

Explanation:

Step1: Convert the mass of one virus to grams

We know that \(1\space mg = 10^{- 3}\space g\).
The mass of one virus \(m_v=9.0\times10^{-12}\space mg\).
Converting to grams: \(m_v = 9.0\times10^{-12}\times10^{-3}\space g=9.0\times10^{-15}\space g\)

Step2: Calculate the mass of 1 mole of viruses

According to Avogadro's number \(N_A = 6.022\times10^{23}\space mol^{-1}\)
The mass of 1 mole of viruses \(M\) is given by \(M = N_A\times m_v\)
Substitute \(N_A = 6.022\times10^{23}\space mol^{-1}\) and \(m_v=9.0\times10^{-15}\space g\)
\(M=(6.022\times10^{23})\times(9.0\times10^{-15})\space g\)
Using the rule of exponents \(a^m\times a^n=a^{m + n}\) and \(a\times b\times10^{m}\times10^{n}=(a\times b)\times10^{m + n}\)
\(M=(6.022\times9.0)\times10^{23-15}\space g\)
\(M = 54.198\times10^{8}\space g\approx5.4\times10^{9}\space g\) (rounded to 2 significant digits)

Step3: Convert the mass of the oil - tanker to grams

The mass of the oil - tanker \(m_t=3.0\times10^{7}\space kg\)
Since \(1\space kg = 10^{3}\space g\), then \(m_t=3.0\times10^{7}\times10^{3}\space g=3.0\times10^{10}\space g\)

Step4: Calculate the number of moles of viruses with the same mass as the oil - tanker

Let \(n\) be the number of moles. We know that \(n=\frac{m_t}{M}\)
Substitute \(m_t = 3.0\times10^{10}\space g\) and \(M = 5.4\times10^{9}\space g/mol\)
\(n=\frac{3.0\times10^{10}}{5.4\times10^{9}}\space mol\)
Using the rule \(\frac{a\times10^{m}}{b\times10^{n}}=\frac{a}{b}\times10^{m - n}\)
\(n=\frac{3.0}{5.4}\times10^{10 - 9}\space mol\)
\(n\approx0.56\times10^{1}\space mol\approx5.6\space mol\) (rounded to 2 significant digits)

Answer:

The mass of 1 mole of viruses is \(5.4\times10^{9}\space g\)
The number of moles of viruses with a mass equal to the mass of an oil - tanker is \(5.6\space mol\)