A sealed cubical container 30.0 cm on a side contains three times Avogadro's number of molecules at a temperature of 20.0°C. Find the force exerted by the gas on one of the walls of the container.

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To find the force exerted by the gas on one of the walls of the container, we can use the ideal gas law and its equation:

PV = nRT

where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature

First, let's find the number of moles of the gas.

Given:
Side length of the container (L) = 30.0 cm = 0.3 m
Volume of the container (V) = L^3 = (0.3 m)^3 = 0.027 m^3

Since the container contains three times Avogadro's number of molecules, we have:
n = 3 * Avogadro's number

The value of Avogadro's number is approximately 6.022 × 10^23 mol⁻¹. So, we can calculate the number of moles:

n = 3 * (6.022 × 10^23) = 1.8066 × 10^24 mol

Next, we need to convert the temperature to Kelvin, as the ideal gas law requires temperature in Kelvin:

Temperature (T) = 20.0°C = 20.0 + 273.15 = 293.15 K

Substituting the values into the ideal gas law equation:

P * V = n * R * T

P * 0.027 m^3 = (1.8066 × 10^24 mol) * (8.314 J/(mol*K)) * 293.15 K

P * 0.027 m^3 = 4.7546 × 10^26 J

Solving for pressure (P):

P = (4.7546 × 10^26 J) / (0.027 m^3)

P = 1.761 × 10^28 Pa

The force exerted on one of the walls of the container is equal to the pressure multiplied by the area of the wall.
Since the container is cubic, the area of one of the walls is given by:

A = L^2 = (0.3 m)^2 = 0.09 m^2

Now we can calculate the force (F):

F = P * A
F = (1.761 × 10^28 Pa) * (0.09 m^2)
F ≈ 1.585 × 10^27 N

Therefore, the force exerted by the gas on one of the walls of the container is approximately 1.585 × 10^27 Newtons.

To find the force exerted by the gas on one of the walls of the container, we need to use the ideal gas law formula:

PV = nRT

where:
P is the pressure of the gas
V is the volume of the gas
n is the number of moles of gas
R is the ideal gas constant
T is the temperature of the gas

First, convert the length of one side of the cube from cm to meters:
30.0 cm = 0.30 m

Next, calculate the volume of the cube:
V = (length)^3
V = (0.30 m)^3
V = 0.027 m^3

The volume of the cube is 0.027 cubic meters.

Now, let's find the number of moles of gas. We are told that the container contains three times Avogadro's number of molecules. Avogadro's number is approximately 6.022 x 10^23.

n = (number of molecules) / (Avogadro's number)
n = (3 x Avogadro's number) / (Avogadro's number)
n = 3 moles

The number of moles of gas is 3 moles.

The temperature we are given is 20.0°C, but we need to convert it to Kelvin since the ideal gas law requires temperature in Kelvin.

To convert from Celsius to Kelvin, use the formula:
T(K) = T(°C) + 273.15

T(K) = 20.0°C + 273.15
T(K) = 293.15 K

Now we have all the values we need to use the ideal gas law.

P * V = n * R * T

R is the ideal gas constant, which is approximately 8.314 J/(mol·K).

Solving for P:
P = (n * R * T) / V
P = (3 moles * 8.314 J/(mol·K) * 293.15 K) / 0.027 m^3

Calculating this expression gives us the pressure of the gas.

Finally, the force exerted by the gas on one of the walls of the container can be found by multiplying the pressure by the area of one of the walls of the cube.

Since the container is a cube, each face has an area equal to the length of one side squared.

Area = (length)^2
Area = (0.30 m)^2
Area = 0.09 m^2

Force = Pressure * Area

By plugging the calculated pressure and area into this equation, you can find the force exerted by the gas on one of the walls of the container.