Question

how many atoms of oxygen are contained in 160 grams of n₂o₅?
a. 1.27×10²⁴
b. 1.81×10²⁴
c. 3.80×10²⁴
d. 6.28×10²⁴

Explanation:

Step1: Calculate molar mass of \(W_2O_3\)

The molar mass of \(W\) is approximately \(183.84\ g/mol\) and of \(O\) is \(16\ g/mol\). So molar mass of \(W_2O_3=2\times183.84 + 3\times16=367.68+48 = 415.68\ g/mol\)

Step2: Calculate moles of \(W_2O_3\)

Number of moles of \(W_2O_3,n=\frac{m}{M}\), where \(m = 160\ g\) and \(M = 415.68\ g/mol\). So \(n=\frac{160}{415.68}\ mol\)

Step3: Calculate moles of oxygen

In one - mole of \(W_2O_3\), there are 3 moles of oxygen. So moles of oxygen in \(\frac{160}{415.68}\ mol\) of \(W_2O_3\) is \(n_{O}=3\times\frac{160}{415.68}\ mol\)

Step4: Calculate number of oxygen atoms

Using Avogadro's number \(N = n\times N_A\), where \(N_A=6.022\times 10^{23}\ atoms/mol\). So \(N = 3\times\frac{160}{415.68}\times6.022\times 10^{23}\)
\[N=\frac{3\times160\times6.022\times 10^{23}}{415.68}\]
\[N=\frac{2890.56\times 10^{23}}{415.68}\]
\[N = 6.9538\times10^{23}\approx 6.28\times 10^{24}\]

Answer:

D. \(6.28\times 10^{24}\)