Respuesta :
Answer:
a) m = 1.174 grams
b) F_g = 0.01151 N
c) F_c = 1013 N
Explanation:
Given:
- The length of a cube L = 10.0 cm
- The molar mass of air M = 28.9 g/mol
- Pressure of air P = 101.3 KPa
- Temperature of air T = 300 K
- Universal Gas constant R = 8.314 J/kgK
Find:
(a) the mass of the gas
(b) the gravitational force exerted on it
(c) the force it exerts on each face of the cube
(d) Why does such a small sample exert such a great force? (6%)
Solution:
- Compute the volume of the cube:
V = L^3 = 0.1^3 = 0.001 m^3
- Use Ideal gas law equation and compute number of moles of air n:
P*V = n*R*T
n = P*V / R*T
n = 101.3*10^3 * 0.001 / 8.314*300
n = 0.04061 moles
- Compute the mass of the gas:
m = n*M
m = 0.04061*28.9
m = 1.174 grams
- The gravitational force exerted on the mass of gas is due to its weight:
F_g = m*g
F_g = 1.174*9.81*10^-3
F_g = 0.01151 N
- The force exerted on each face of cube is due its surface area:
F_c = P*A
F_c = (101.3*10^3)*(0.1)^2
F_c = 1013 N
- The molecules of a gas have high kinetic energy; hence, high momentum. When they collide with the walls they transfer momentum per unit time as force. Higher the velocity of the particles higher the momentum higher the force exerted.
(a) The mass of the gas is 1.174g
(b) Gravitational force on it is 0.0115N
(c) Force exerted on the container walls is 1.01×10³N
(d) High kinetic energy of the molecules
Ideal gas in a container:
The sides of the cubical container are, L = 10cm = 0.1m
Pressure of the gas, P = 1 atm = 1.01×10⁵ Pa
Temperature of the gas, T = 300K
Molas mass, M = 28.9 g/mol
(a) The volume of the container:
V = L³ = 0.1³
V = 0.001m³
From the idea gas equation:
PV = nRT
n = PV/RT
n = (1.01×10⁵)(0.001)/8.314×300
n = 0.04061 moles
So, the mass of the gas is:
m = nM = 0.04061×28.9
m = 1.174g
(b) the gravitaitonal force on the gas is given by:
f = mg
f = 1.174×10⁻³×9.8
f = 0.0115N
(c) the force exerted on each wall of the cube is :
F = PA
where A is the area of each wall
F = 1.01×10⁵×0.1×0.1
F = 1.01×10³ N
(d) The atoms/molecules of the gas have high kinetic energies, they constantly collide with the walls of the container and transfer large momentum which results in such large force.
Learn more about ideal gas:
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