To solve this problem, we can use the concept of the ideal gas law, which states that the product of the pressure, volume, and the number of moles of a gas is proportional to the temperature. Mathematically, it can be represented as:
PV = nRT
where: P = pressure V = volume n = number of moles R = ideal gas constant T = temperature
In this case, we are given that the temperature and pressure remain the same. So we can write the equation as:
P₁V₁ = n₁RT P₂V₂ = n₂RT
We want to find n₂, the number of moles in a 20 L sample. Let's substitute the given values into the equation:
P₁ = P₂ (pressure remains the same) V₁ = 7.25 L n₁ = 0.75 mole V₂ = 20 L R = ideal gas constant (a known value) T = temperature (remains the same)
Using the above information, we can set up the equation as follows:
P₁V₁ = n₁RT P₂V₂ = n₂RT
Since P₁ = P₂ and T remains the same, we can simplify the equation to:
V₁ / n₁ = V₂ / n₂
Now we can solve for n₂:
n₂ = (V₂ * n₁) / V₁
Substituting the given values:
n₂ = (20 L * 0.75 mole) / 7.25 L
Calculating this expression gives us:
n₂ = 2.06 moles
Therefore, there would be approximately 2.06 moles of nitrogen in a 20 L sample, assuming the temperature and pressure remain the same.