An ideal gas has a pressure of 2.5 atm,a volume of 1.0 L at a temperature of 30$^{\circ}$C.How many molecules are there in the gas? A) 6.1 $\times$ 10²³ B) 6.0 $\times$ 10²³ C) 2.4 $\times$ 10²³ D) 2.3 $\times$ 10²³

Question

Quizplus · Accepted Answer

We can use the ideal gas law: PV = nRT
where P = 2.5 atm, V = 1.0 L, R is the gas constant, and T is the temperature converted to Kelvin: 
T = (30°C + 273.15) K = 303.15 K
Substituting these values, we get: 
(2.5 atm)(1.0 L) = n(0.0821 L⋅atm/mol⋅K)(303.15 K)
Solving for n, the number of moles of gas: 
n = 0.1033 mol
To convert from moles to molecules, we use Avogadro's number: 
1 mol = 6.022 × 10^23 molecules
Therefore, the number of molecules in the gas is: 
(0.1033 mol)(6.022 × 10^23 molecules/mol) = 6.21 × 10^22 molecules, which is closest to answer choice B, 6.0 × 10^22 molecules.

An Ideal Gas Has a Pressure of 2 ∘^{\circ}∘ CHow Many Molecules Are There in the Gas? A) 6

An Ideal Gas Has a Pressure of 2 $^{\circ}$ CHow Many Molecules Are There in the Gas?
A) 6