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 \(1\space mg = 10^{- 3}\space g\). So, the mass of one virus \(m_v=9.0\times10^{-12}\space mg=9.0\times10^{-12}\times10^{- 3}\space g = 9.0\times10^{-15}\space g\)

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 \(M = N_A\times m_v\)

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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 \(n=\frac{m_t}{M}\)

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Answer:

The mass of 1 mole of viruses is \(5.4\times 10^{9}\space g\) and the number of moles of viruses with a mass equal to that of the oil - tanker is \(0.56\space mol\)