Question

a scientist is determining the mass of 38,000 molecules of oxygen. use this to answer parts a and b. a. how many significant digits should be in the solution? there should be 2 significant digits in the solution. (type a whole number.) b. express the mass of 38,000 molecules of oxygen in scientific notation. \boxed{} grams (type your answer using the appropriate number of significant digits. type your an

Explanation:

To solve part b, we first need to recall the molar mass of oxygen and Avogadro's number. The molar mass of \(O_2\) (oxygen gas) is approximately \(32\space g/mol\), and Avogadro's number is \(6.022\times10^{23}\space molecules/mol\).

Step 1: Calculate the number of moles

The number of moles \(n\) of oxygen molecules is given by the formula \(n=\frac{N}{N_A}\), where \(N = 38000 = 3.8\times10^{4}\space molecules\) and \(N_A=6.022\times10^{23}\space molecules/mol\).

$$ n=\frac{3.8\times 10^{4}}{6.022\times 10^{23}} $$

Step 2: Calculate the mass

The mass \(m\) is given by \(m = n\times M\), where \(M = 32\space g/mol\) (molar mass of \(O_2\)).

$$ m=\frac{3.8\times 10^{4}}{6.022\times 10^{23}}\times32 $$

First, calculate \(\frac{3.8\times32}{6.022}\approx\frac{121.6}{6.022}\approx20.19\)

Then, for the exponents: \(10^{4 - 23}=10^{-19}\)

So, \(m\approx20.19\times 10^{-19}\space g\)

Now, we need to express this in scientific notation with 2 significant digits.

\(20.19\times 10^{-19}=2.019\times 10^{1}\times 10^{-19}=2.019\times 10^{-18}\space g\)

Rounding to 2 significant digits, we get \(2.0\times 10^{-18}\space g\)

Answer:

\(2.0\times 10^{-18}\)