Volume of Gas Molecules in 3D Box given Pressure Calculator

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✖The Number of Molecules is the total number of particles present in the specific container.ⓘ Number of Molecules [N_molecules]			+10% -10%
✖The Mass of Each Molecule is the ratio of molar mass and Avagadro number.ⓘ Mass of Each Molecule [m]			+10% -10%
✖The Root Mean Square Speed is the value of the square root of the sum of the squares of the stacking velocity values divided by the number of values.ⓘ Root Mean Square Speed [C_RMS]			+10% -10%
✖The pressure of Gas is the force that the gas exerts on the walls of its container.ⓘ Pressure of Gas [P_gas]			+10% -10%

✖The volume of Gas is the amount of space that it occupies.ⓘ Volume of Gas Molecules in 3D Box given Pressure [V_gas]

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Formula

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Volume of Gas Molecules in 3D Box given Pressure

Formula

`"V"_{"gas"} = (1/3)*(("N"_{"molecules"}*"m"*("C"_{"RMS"})^2)/"P"_{"gas"})`

Example

`"1550.388L"=(1/3)*(("100"*"0.1g"*("10m/s")^2)/"0.215Pa")`

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Download Kinetic Theory of Gases Formula PDF

Volume of Gas Molecules in 3D Box given Pressure Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume of Gas = (1/3)*((Number of Molecules*Mass of Each Molecule*(Root Mean Square Speed)^2)/Pressure of Gas)
V_gas = (1/3)*((N_molecules*m*(C_RMS)^2)/P_gas)
This formula uses 5 Variables

Variables Used

Volume of Gas - (Measured in Cubic Meter) - The volume of Gas is the amount of space that it occupies.
Number of Molecules - The Number of Molecules is the total number of particles present in the specific container.
Mass of Each Molecule - (Measured in Kilogram) - The Mass of Each Molecule is the ratio of molar mass and Avagadro number.
Root Mean Square Speed - (Measured in Meter per Second) - The Root Mean Square Speed is the value of the square root of the sum of the squares of the stacking velocity values divided by the number of values.
Pressure of Gas - (Measured in Pascal) - The pressure of Gas is the force that the gas exerts on the walls of its container.

STEP 1: Convert Input(s) to Base Unit

Number of Molecules: 100 --> No Conversion Required
Mass of Each Molecule: 0.1 Gram --> 0.0001 Kilogram (Check conversion here)
Root Mean Square Speed: 10 Meter per Second --> 10 Meter per Second No Conversion Required
Pressure of Gas: 0.215 Pascal --> 0.215 Pascal No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V_gas = (1/3)*((N_molecules*m*(C_RMS)^2)/P_gas) --> (1/3)*((100*0.0001*(10)^2)/0.215)

Evaluating ... ...

V_gas = 1.55038759689922

STEP 3: Convert Result to Output's Unit

1.55038759689922 Cubic Meter -->1550.38759689922 Liter (Check conversion here)

FINAL ANSWER

1550.38759689922 ≈ 1550.388 Liter <-- Volume of Gas

(Calculation completed in 00.020 seconds)

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K J Somaiya College of science (K J Somaiya), Mumbai

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< 9 Volume of Gas Calculators

Volume of Gas Molecules in 3D Box given Pressure

Go Volume of Gas = (1/3)*((Number of Molecules*Mass of Each Molecule*(Root Mean Square Speed)^2)/Pressure of Gas)

Volume of Gas given Average Velocity and Pressure in 2D

Go Volume of Gas = (Molar Mass*2*((Average Velocity of Gas)^2))/(pi*Pressure of Gas)

Volume of Gas given Average Velocity and Pressure

Go Volume of Gas = (Molar Mass*pi*((Average Velocity of Gas)^2))/(8*Pressure of Gas)

Volume of Gas given Most Probable Speed and Pressure

Go Volume of Gas = (Molar Mass*((Most Probable Velocity)^2))/(2*Pressure of Gas)

Volume of Gas given Root Mean Square Speed and Pressure in 2D

Go Volume of Gas = ((Root Mean Square Speed)^2)*Molar Mass/(2*Pressure of Gas)

Volume of Gas given Most Probable Speed and Pressure in 2D

Go Volume of Gas = (Molar Mass*((Most Probable Velocity)^2))/(Pressure of Gas)

Volume of Gas given Root Mean Square Speed and Pressure

Go Volume of Gas = ((Root Mean Square Speed)^2)*Molar Mass/(3*Pressure of Gas)

Volume of Gas given Root Mean Square Speed and Pressure in 1D

Go Volume of Gas = ((Root Mean Square Speed)^2)*Molar Mass/(Pressure of Gas)

Volume of Gas given Kinetic Energy

Go Volume of Gas = (2/3)*(Kinetic Energy/Pressure of Gas)

Volume of Gas Molecules in 3D Box given Pressure Formula

Volume of Gas = (1/3)*((Number of Molecules*Mass of Each Molecule*(Root Mean Square Speed)^2)/Pressure of Gas)
V_gas = (1/3)*((N_molecules*m*(C_RMS)^2)/P_gas)

What are the postulates of kinetic theory of gases?

1) Actual volume of gas molecules is negligible in comparison to the total volume of the gas. 2) no force of attraction between the gas molecules. 3) Particles of gas are in constant random motion. 4) Particles of gas collide with each other and with the walls of the container. 5)Collisions are perfectly elastic. 6) Different particles of the gas, have different speeds. 7) The average kinetic energy of the gas molecule is directly proportional to the absolute temperature.

How to Calculate Volume of Gas Molecules in 3D Box given Pressure?

Volume of Gas Molecules in 3D Box given Pressure calculator uses Volume of Gas = (1/3)*((Number of Molecules*Mass of Each Molecule*(Root Mean Square Speed)^2)/Pressure of Gas) to calculate the Volume of Gas, The volume of gas molecules in 3D box given pressure formula is defined as one-third of the ratio of root mean square speed of each molecule and pressure of the gas. Volume of Gas is denoted by V_gas symbol.

How to calculate Volume of Gas Molecules in 3D Box given Pressure using this online calculator? To use this online calculator for Volume of Gas Molecules in 3D Box given Pressure, enter Number of Molecules (N_molecules), Mass of Each Molecule (m), Root Mean Square Speed (C_RMS) & Pressure of Gas (P_gas) and hit the calculate button. Here is how the Volume of Gas Molecules in 3D Box given Pressure calculation can be explained with given input values -> 1.6E+6 = (1/3)*((100*0.0001*(10)^2)/0.215).

FAQ

What is Volume of Gas Molecules in 3D Box given Pressure?

The volume of gas molecules in 3D box given pressure formula is defined as one-third of the ratio of root mean square speed of each molecule and pressure of the gas and is represented as V_gas = (1/3)*((N_molecules*m*(C_RMS)^2)/P_gas) or Volume of Gas = (1/3)*((Number of Molecules*Mass of Each Molecule*(Root Mean Square Speed)^2)/Pressure of Gas). The Number of Molecules is the total number of particles present in the specific container, The Mass of Each Molecule is the ratio of molar mass and Avagadro number, The Root Mean Square Speed is the value of the square root of the sum of the squares of the stacking velocity values divided by the number of values & The pressure of Gas is the force that the gas exerts on the walls of its container.

How to calculate Volume of Gas Molecules in 3D Box given Pressure?

The volume of gas molecules in 3D box given pressure formula is defined as one-third of the ratio of root mean square speed of each molecule and pressure of the gas is calculated using Volume of Gas = (1/3)*((Number of Molecules*Mass of Each Molecule*(Root Mean Square Speed)^2)/Pressure of Gas). To calculate Volume of Gas Molecules in 3D Box given Pressure, you need Number of Molecules (N_molecules), Mass of Each Molecule (m), Root Mean Square Speed (C_RMS) & Pressure of Gas (P_gas). With our tool, you need to enter the respective value for Number of Molecules, Mass of Each Molecule, Root Mean Square Speed & Pressure of Gas and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Volume of Gas?

In this formula, Volume of Gas uses Number of Molecules, Mass of Each Molecule, Root Mean Square Speed & Pressure of Gas. We can use 8 other way(s) to calculate the same, which is/are as follows -

Volume of Gas = (Molar Mass*pi*((Average Velocity of Gas)^2))/(8*Pressure of Gas)
Volume of Gas = (Molar Mass*2*((Average Velocity of Gas)^2))/(pi*Pressure of Gas)
Volume of Gas = (2/3)*(Kinetic Energy/Pressure of Gas)
Volume of Gas = (Molar Mass*((Most Probable Velocity)^2))/(2*Pressure of Gas)
Volume of Gas = (Molar Mass*((Most Probable Velocity)^2))/(Pressure of Gas)
Volume of Gas = ((Root Mean Square Speed)^2)*Molar Mass/(3*Pressure of Gas)
Volume of Gas = ((Root Mean Square Speed)^2)*Molar Mass/(Pressure of Gas)
Volume of Gas = ((Root Mean Square Speed)^2)*Molar Mass/(2*Pressure of Gas)

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