Question

an oxygen atom has a mass of ( 2.66\times10^{-23} ) g and a glass of water has a mass of 0.050 kg. use this information to answer the questions below. be sure your answers have the correct number of significant what is the mass of 1 mole of oxygen atoms? round your answer to 3 significant digits. g how many moles of oxygen atoms have a mass equal to the mass of a glass of water? round your answer to 2 significant digits.

Explanation:

Step1: Calculate the mass of 1 mole of oxygen atoms

Avogadro's number \(N_A = 6.022\times10^{23}\text{ mol}^{-1}\).
The mass of one oxygen atom \(m = 2.66\times 10^{-23}\text{ g}\).
The mass of 1 mole of oxygen atoms \(M=m\times N_A\).

$$M=(2.66\times 10^{-23}\text{ g})\times(6.022\times 10^{23}\text{ mol}^{-1})$$

$$M = 2.66\times6.022\text{ g/mol}$$

$$M\approx16.0\text{ g/mol}$$

Step2: Calculate the number of moles of oxygen atoms with a mass equal to the mass of the glass of water

The mass of the glass of water \(m_{water}=0.050\text{ kg}=50\text{ g}\).
Using the formula \(n=\frac{m}{M}\), where \(M = 16.0\text{ g/mol}\) (from step 1) and \(m = 50\text{ g}\).

$$n=\frac{50\text{ g}}{16.0\text{ g/mol}}$$

$$n=\frac{50}{16.0}\text{ mol}$$

$$n\approx3.1\text{ mol}$$

Answer:

The mass of 1 mole of oxygen atoms is \(16.0\text{ g}\).
The number of moles of oxygen atoms with a mass equal to the mass of the glass of water is \(3.1\text{ mol}\).