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c(rms)=√(3RT/M) for problems when no of moles is not 1?

Because I think the mole will be deduced as

c(rms)=√(3nRT/nM) =√(3RT/M)

For instance I found this problem, given atmospheric pressure is 10^5 Pa, molecular mass of

Nitrogen is 28, and at STP the density is 1.25 kg/m^3. What is the c(rms) at 100°C?

If the problem is solved with c(rms)=√(3P/rho) the answer is 576.35 which is the actual answer, and when taken the above equation the answer is 18.22

Then what's wrong with my concept?