calculate the pressure (in Pascals and bar) of 10^23 gas particles each with a mass of 10^-25 kg, in a 1 L container if the rms speed is 100m/s? What is the total kinetic energy of these particles? What is the temperature inside the container
u(rms) = sqrt(3RT/M)
Solve for M = molar mass
# particles x mass of each = grams
g/molar mass = #moles = n
Then use PV = nRT and convert P from atom to Pa and bar.
But the problem didn't give temperature that is qhat confused me
To calculate the pressure of the gas particles in Pascals and bar, we can use the ideal gas law:
PV = nRT
Where:
P = Pressure (in Pascals)
V = Volume (in cubic meters)
n = Number of gas particles (in moles)
R = Ideal gas constant (in J/(mol·K))
T = Temperature (in Kelvin)
First, let's calculate the number of moles (n) of gas particles in the container. Since we are given the mass of each particle, we can use the molar mass to convert it to moles.
The molar mass (M) can be calculated using the formula:
M = mass / N_A
Where:
mass = Mass of a single particle (in kg)
N_A = Avogadro's number (6.022 × 10^23 particles/mol)
Plugging in the values, we get:
M = 10^(-25) kg / (6.022 × 10^23 particles/mol)
Now, let's calculate the number of moles. Given that there are 10^23 gas particles in the container:
n = (10^23 particles) / (6.022 × 10^23 particles/mol)
With the volume of the container as 1 L, we need to convert it to cubic meters:
V = 1 L = 0.001 m^3
Now, let's calculate the pressure (P) using the ideal gas law:
P = (nRT) / V
The ideal gas constant (R) is 8.314 J/(mol·K).
To convert the pressure from Pascals to bar, divide by 10^5 since 1 bar = 10^5 Pa.
For the total kinetic energy of the particles, we can use the following formula:
KE_total = (3/2) * n * k * T
Where:
n = Number of particles (in moles)
k = Boltzmann constant (1.381 × 10^-23 J/K)
T = Temperature (in Kelvin)
To find the temperature (T), we can rearrange the ideal gas law equation:
T = (PV) / (nR)
Now, let's plug in the calculated values and solve the equations to find the pressure, total kinetic energy, and temperature.