A flexible container at an initial volume of 5.12 L contains 7.51 mol of gas. More gas is then added to the container until it reaches a final volume of 18.3 L. Assuming the pressure and temperature of the gas remain constant, calculate the number of moles of gas added to the container.
Well, well, well! Looks like our flexible container has gone from a modest 5.12 L to a whopping 18.3 L! Talk about a growth spurt!
Now, since the pressure and temperature of the gas remain constant, we can apply a handy little equation called Avogadro's law. It states that equal volumes of gases, at the same pressure and temperature, contain the same number of molecules. Fancy stuff!
So, to find the number of moles of gas we've added, we just need to compare the initial volume and moles of gas to the final volume. Let's do some math magic!
Initial moles of gas = 7.51 mol
Initial volume = 5.12 L
Final volume = 18.3 L
Since moles of gas remain constant, we can set up a proportion:
Initial volume / Initial moles of gas = Final volume / X (X being the number of moles of gas added)
Plugging in the values:
5.12 L / 7.51 mol = 18.3 L / X
Cross-multiplying:
5.12 L * X = 7.51 mol * 18.3 L
And solving for X:
X = (7.51 mol * 18.3 L) / 5.12 L
Crunching those numbers, we find:
X ≈ 26.842 mol
Eureka! We've added approximately 26.842 moles of gas to our flexible container. That's enough moles to throw one crazy party in there! Time to break out the gas balloons!
To find the number of moles of gas added to the container, we can use the ideal gas law equation, which states: PV = nRT.
Given:
Initial volume, V₁ = 5.12 L
Initial number of moles, n₁ = 7.51 mol
Final volume, V₂ = 18.3 L
Since the pressure and temperature of the gas remain constant, we can rewrite the equation as:
n₁ / V₁ = n₂ / V₂
where n₂ represents the number of moles of gas added.
Rearranging the equation to solve for n₂:
n₂ = (n₁ × V₂) / V₁
Substituting the given values:
n₂ = (7.51 mol × 18.3 L) / 5.12 L
n₂ = 26.733 mol
Therefore, approximately 26.733 moles of gas were added to the container.
1.5
(V1/n1)=(V2/n2)
(5.12÷7.51)=18.3÷n2
n2=26.84mol