Imagine that you have an ideal gas in a 8.00L container, and that 2850 molecules of this gas collide with a square-inch area of the container at any given instant.
If the volume is increased to 56.0L at constant temperature, how many collisions will occur per square inch of this larger container?
How do we do this step by step?
To determine the number of collisions per square inch in the larger container, we need to compare the ratio of the square inch areas of the two containers.
Here's a step-by-step process:
Step 1: Find the number of collisions per square inch in the initial container.
- We are given that 2850 molecules collide with a square-inch area of the initial 8.00L container at any given instant.
- Therefore, the number of collisions per square inch in the initial container is 2850.
Step 2: Calculate the ratio of the volumes of the two containers.
- The volume of the initial container is 8.00L, and the volume of the larger container is 56.0L.
- To find the ratio, divide the volume of the larger container by the volume of the initial container: 56.0L / 8.00L = 7.
Step 3: Square the ratio obtained in Step 2 to determine the ratio of the square inch areas.
- Since the ratio was obtained by dividing the larger volume by the initial volume, we need to square it to find the ratio of the areas: 7^2 = 49.
Step 4: Multiply the number of collisions per square inch in the initial container by the area ratio from Step 3.
- Multiply the number of collisions per square inch in the initial container (2850) by the area ratio (49): 2850 * 49 = 139,650.
Step 5: Interpret the result.
- The number of collisions per square inch in the larger container is 139,650.
Therefore, at a constant temperature and with an increase in volume from 8.00L to 56.0L, there would be 139,650 collisions per square inch in the larger container.