Answer :

We start by noting that at room temperature and pressure the molar volume of a gas is approximately

[tex]$$
V_m = 24.0 \, \text{dm}^3/\text{mol}.
$$[/tex]

Given a volume of

[tex]$$
V = 6.00 \, \text{dm}^3,
$$[/tex]

we can calculate the number of moles of carbon dioxide ([tex]$\text{CO}_2$[/tex]) gas using the formula

[tex]$$
n = \frac{V}{V_m} = \frac{6.00 \, \text{dm}^3}{24.0 \, \text{dm}^3/\text{mol}} = 0.25 \, \text{mol}.
$$[/tex]

Next, we use Avogadro's number,

[tex]$$
N_A = 6.02214076 \times 10^{23} \, \text{molecules/mol},
$$[/tex]

to convert the number of moles into the number of molecules:

[tex]$$
\text{Number of molecules} = n \times N_A = 0.25 \, \text{mol} \times 6.02214076 \times 10^{23} \, \text{molecules/mol}.
$$[/tex]

This yields

[tex]$$
\text{Number of molecules} \approx 1.50553519 \times 10^{23} \, \text{molecules}.
$$[/tex]

Thus, there are approximately

[tex]$$
1.50553519 \times 10^{23}
$$[/tex]

molecules of carbon dioxide in 6.00 dm³ at room temperature and pressure.

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