Which of the following gas samples would have the largest volume, if all samples are at the same temperature and pressure?

a. 5×1023 molecules of N2
b. 0.306 moles CO2
c. 40.4 grams of Ne
d. they would all have the same volume

c. 40.4 grams of Ne

Explanation:

Let's consider the ideal gas law.

P × V = n × R × T

V = n × R × T/P

As we can see, when the samples have the same temperature and pressure, the volume is directly proportional to the number of moles. The higher the number of moles, the larger the volume.

a.

1 mole of N₂ contains 6.02 × 10²³ molecules of N₂. The moles corresponding to 5 × 10²³ molecules of N₂ are:

5 × 10²³ molecules × (1 mol/6.02 × 10²³ molecules) = 0.8 mol

b. 0.306 moles CO₂

c. The molar mass of Ne is 20.18 g/mol. The moles corresponding to 40.4 g of Ne are:

40.4 g × (1 mol/20.18 g) = 2.00 mol

The sample of Ne is the one with the higher number of moles, therefore it has the largest volume.

i believe the answer is a.