A sample consisting of 22.7 g of a nongaseous, unstable compound X is placed inside a metal cylinder with a radius of 8.00 cm, and a piston is carefully placed on the surface of the compound so that, for all practicla purposes, the distance between the bottom of the cylinder and the piston is zero. (A hole in the piston allows trapped air to escape as the piston is placed on the compound; then this hole is pulugged so that nothing inside the cylinder can escape.) The piston-and-cylinder apparatus is carefully placed in 10.00kg of water at 25.00 degrees C. The barometric pressure is 778 torr.
To find the pressure inside the cylinder, we need to consider the different factors that contribute to the total pressure.
1. The pressure due to the weight of the water:
The weight of the water can be calculated using the formula:
Weight = mass × gravity
Given that the mass of water is 10.00 kg and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the weight of the water.
2. The atmospheric pressure:
The atmospheric pressure is given as 778 torr.
3. The pressure due to the compound X:
To calculate the pressure due to the compound X, we need to use the ideal gas law equation:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = gas constant
T = temperature
We are given the mass of compound X, so we need to determine the number of moles of the compound. To do this, we can use the molar mass of X.
4. The pressure due to the piston:
Since the distance between the bottom of the cylinder and the piston is effectively zero, the pressure applied by the piston will contribute to the total pressure.
To calculate this pressure, we can use the formula:
Pressure = Force / Area
To find the force, we can use the weight of the compound X calculated from its mass and the acceleration due to gravity. The area can be calculated using the radius of the cylinder.
By adding up these pressures, we can determine the total pressure inside the cylinder.