Question

1. a sample contains 1.25mol of nitrogen dioxide, co₂

a) how many molecules are in the sample?(ans.7.52×10²³ molecules)
b) how many atoms are in the sample?(ans.2.26×10²⁴ atoms)

1. converting number of particles to moles

n = nₐ × n
n = \frac{n}{nₐ}

Explanation:

Step1: Recall the formula for molecules

The formula to find the number of molecules \( N \) is \( N = N_A\times n \), where \( N_A = 6.022\times 10^{23}\space mol^{-1} \) (Avogadro's number) and \( n \) is the number of moles. Given \( n = 1.25\space mol \).

Step2: Calculate number of molecules

Substitute the values into the formula: \( N=(6.022\times 10^{23})\times(1.25) \).
\( N = 7.5275\times 10^{23}\approx7.52\times 10^{23} \) molecules (matching the given answer for part a).

Step3: Recall atoms in \( \text{CO}_2 \)

Each \( \text{CO}_2 \) molecule has 3 atoms (1 C and 2 O). So if number of molecules is \( N \), number of atoms \( = 3\times N \).

Step4: Calculate number of atoms

We know \( N = 7.52\times 10^{23} \) molecules. So number of atoms \( = 3\times7.52\times 10^{23}=2.256\times 10^{24}\approx2.26\times 10^{24} \) atoms (matching the given answer for part b).

Answer:

a) The number of \( \text{CO}_2 \) molecules is \( \boldsymbol{7.52\times 10^{23}} \).
b) The number of atoms in the sample is \( \boldsymbol{2.26\times 10^{24}} \).