The pressure of a sample of an inert gas reduced significantly from 100 kPa to 30kPa. The temperature increases from 27degreeC to 93degreeC. If the initial volume is 20 L, what is the final volume?
81 L
54.2 L
96 L
55 L
Well, it seems like the gas was feeling a bit deflated, going from 100 kPa to 30 kPa. I guess it just couldn't handle the pressure!
But fear not, my friend! The temperature decided to lend a helping hand by increasing from 27 degrees Celsius to 93 degrees Celsius. Talk about a hot topic!
Now, with all these changes going on, let's see what the final volume is. Since the initial volume is 20 L, let's crunch some numbers and find the answer!
*Drumroll, please*
Ta-dah! The final volume is...
54.2 L!
It looks like this gas had a change of heart and decided to occupy a smaller space. Good for it, I guess. Just shows you never know what gases are up to these days!
To solve this problem, we can use the combined gas law formula:
(P₁ x V₁) / T₁ = (P₂ x V₂) / T₂
Given:
P₁ = 100 kPa (initial pressure)
V₁ = 20 L (initial volume)
T₁ = 27 °C + 273.15 (initial temperature in Kelvin)
P₂ = 30 kPa (final pressure)
T₂ = 93 °C + 273.15 (final temperature in Kelvin)
Plugging in the values into the formula, we have:
(100 kPa x 20 L) / (27 °C + 273.15) = (30 kPa x V₂) / (93 °C + 273.15)
Simplifying the equation, we get:
(2000 kPa L) / (300.15 K) = (30 kPa x V₂) / (366.15 K)
Cross-multiplying, we have:
(2000 kPa L) x (366.15 K) = (30 kPa) x V₂ x (300.15 K)
730300 kPa L K = 9004.5 kPa L x V₂
Dividing both sides by 9004.5 kPa L, we get:
V₂ = 730300 kPa L K / 9004.5 kPa L
V₂ ≈ 81 L
Therefore, the final volume is approximately 81 L.
To find the final volume of the gas, we need to use the combined gas law equation:
P1V1/T1 = P2V2/T2
Where:
P1 is the initial pressure (100 kPa)
V1 is the initial volume (20 L)
T1 is the initial temperature in Kelvin (27°C + 273.15)
P2 is the final pressure (30 kPa)
T2 is the final temperature in Kelvin (93°C + 273.15)
First, let's convert the initial temperature to Kelvin:
T1 = 27°C + 273.15 = 300.15 K
Next, let's convert the final temperature to Kelvin:
T2 = 93°C + 273.15 = 366.15 K
Now, we can substitute these values into the combined gas law equation:
(100 kPa)(20 L)/(300.15 K) = (30 kPa)(V2)/(366.15 K)
We can solve for V2 by rearranging the equation:
V2 = (100 kPa)(20 L)(366.15 K)/(300.15 K)(30 kPa)
V2 ≈ 96.1 L
Therefore, the final volume of the gas is approximately 96.1 L. So, the closest option is 96 L.