Imagine that you have an ideal gas in a 4.80L container, and that 2450 molecules of this gas collide with a square-inch area of the container at any given instant.
If the volume is increased to 19.2L at constant temperature, how many collisions will occur per square inch of this larger container?
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I'm not sure
To find the number of collisions per square inch in the larger container, we need to use the concept of ideal gas law and the relationship between volume and the number of gas molecules.
The ideal gas law states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature.
In this case, we are given that there are 2450 molecules of gas, and we need to find the number of collisions per square inch in the larger container when the volume is increased to 19.2L.
To calculate the number of collisions, we can use the relationship between the volume and the number of gas molecules.
First, we need to determine the initial number of moles of gas in the 4.80L container. We can use the ideal gas law rearranged to solve for n:
n = PV / RT
Let's assume the temperature is constant, so we can ignore it for now. The pressure is not given, but since we're only interested in the number of collisions per square inch, the pressure is not necessary.
So, let's calculate the initial number of moles of gas:
n = (4.80L) x (1 mole / 22.4L) = 0.2143 mole
Now, the volume is increased to 19.2L. We can calculate the final number of moles using the same formula:
n = (19.2L) x (1 mole / 22.4L) = 0.8571 mole
To find the number of collisions in the larger container, we need to calculate the ratio of the final number of moles to the initial number of moles:
0.8571 mole / 0.2143 mole = 4
Therefore, there will be 4 times as many collisions in the larger container compared to the initial container.
Since we were given that there were 2450 collisions per square inch in the initial container, we can multiply that by 4 to find the number of collisions per square inch in the larger container:
2450 collisions/in^2 x 4 = 9800 collisions/in^2
Therefore, there will be 9800 collisions per square inch in the larger container.