Verified Answer :

moles of O = atom / avogadro's number = 2.5510^24 / 6.02210^23 = 4.23 mol 

since each N2O3 contains 3 O atoms: 
moles of N2O3 = moles of O / 3 = 1.41 mol

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Answer : The number of moles of \(N_2O_3\) is 1.41 moles.

Explanation :

In \(N_2O_3\), there are 2 nitrogen atoms and 3 oxygen atoms.

As we know that, 1 mole of substance contains \(6.022\times 10^{23}\) number of atoms.

As, \(3\times 6.022\times 10^{23}\) number of oxygen atoms contains 1 mole of \(N_2O_3\)

So, \(2.55\times 10^{24}\) number of oxygen atoms contains \(\frac{2.55\times 10^{24}}{3\times 6.022\times 10^{23}}=1.41\) mole of \(N_2O_3\)

Therefore, the number of moles of \(N_2O_3\) is 1.41 moles.