what will the volume of a gas at 309K if its volume at 215K is 3.42 L? Assume the pressure is constant
V = 3.42L * (309k/215k) = 4.92 L.
Oh, the poor little gas! It's feeling so hot and bothered at 309K, isn't it? Well, fear not, my friend. We can calculate its new volume using Charles' Law. Charles was a clever scientist who found out that when the pressure is constant, the volume of a gas is directly proportional to its temperature. What a genius!
Now, let's plug in those numbers and work our magic. If the gas has a volume of 3.42 L at 215K, and we want to know its volume at 309K, we can set up a proportion:
215K/3.42L = 309K/x
Now, let's cross multiply and solve for x (the new volume):
215K * x = 309K * 3.42L
x = (309K * 3.42L) / 215K
And the grand finale... *drum roll*... the new volume is approximately 4.91 L!
So, there you have it. The gas expands and fills up a spacious 4.91 L at 309K. Isn't science marvelous?
To solve this problem, we can use Charles's Law, which states that the volume of a gas is directly proportional to its temperature in Kelvin if the pressure is constant.
The formula for Charles's Law is:
V1 / T1 = V2 / T2
Where:
V1 = initial volume of the gas (in this case, 3.42 L)
T1 = initial temperature of the gas (in this case, 215 K)
V2 = final volume of the gas (which we need to find)
T2 = final temperature of the gas (in this case, 309 K)
Rearranging the equation, we have:
V2 = (V1 * T2) / T1
Now we can substitute the known values into the equation:
V2 = (3.42 L * 309 K) / 215 K
Calculating this expression gives us:
V2 = 4.91 L
Therefore, the volume of the gas at 309 K would be 4.91 L, assuming the pressure remains constant.
To solve this problem, we can make use of the relationship between volume and temperature known as Charles' Law which states that the volume of a gas is directly proportional to its temperature, assuming constant pressure.
Charles' Law can be expressed as:
V1 / T1 = V2 / T2
Where:
V1 = Initial volume of the gas
T1 = Initial temperature of the gas
V2 = Final volume of the gas
T2 = Final temperature of the gas
In this case, we know the initial volume (V1) is 3.42 L, the initial temperature (T1) is 215 K, and we want to find the final volume (V2) when the temperature (T2) is 309 K.
Let's plug in the values into the equation:
3.42 L / 215 K = V2 / 309 K
To solve for V2, we cross-multiply:
(3.42 L) * (309 K) = (215 K) * V2
Calculation:
1,056.78 L*K = 46,335 K * V2
Now, divide both sides by 46,335 K to isolate V2:
V2 = 1,056.78 L*K / 46,335 K
Simplifying the equation:
V2 ≈ 0.0228 L
Therefore, the volume of the gas at 309 K is approximately 0.0228 L.