# Calculating rms speed of hydrogen molecules

• amw2829
In summary: J(thermal energyinitial) + 500 J - 2000 = E thermalfinal = 5/3(1/2)mv23000 J was the initial thermal energy . It decreased by 1500 J, the final thermal energy is 1500 J. The thermal energy is 5/3 (1/2 mv^2). So how much is 1/2 mv^2, the translational kinetic energy? How much is v, the rms speed? 1/2 mv^2 = (5/3)(1/2)mv^2 = v
amw2829

## Homework Statement

The rms speed of the molecules in 1.1 g of hydrogen gas is 1800 m/s.

500 J of work are done to compress the gas while, in the same process, 2000 J of heat energy are transferred from the gas to the environment. Afterward, what is the rms speed of the molecules?

I've already solved for the total translational energy(1800 J) before more work was done to the molecules. The thermal energy was also 3000 J.

## Homework Equations

E = (5/3)(1/2)mv^2

## The Attempt at a Solution

Since 500 J are compressed, and 2000 J are released, the energy would then be 300 J. I tried setting this equal to the above equation, but all answers I entered were wrong.

amw2829 said:

## Homework Statement

The rms speed of the molecules in 1.1 g of hydrogen gas is 1800 m/s.

500 J of work are done to compress the gas while, in the same process, 2000 J of heat energy are transferred from the gas to the environment. Afterward, what is the rms speed of the molecules?

I've already solved for the total translational energy(1800 J) before more work was done to the molecules. The thermal energy was also 3000 J.

## The Attempt at a Solution

Since 500 J are compressed, and 2000 J are released, the energy would then be 300 J. I tried setting this equal to the above equation, but all answers I entered were wrong.

300 J as final energy is wrong.
When compressing, work is done on the gas, increasing the internal energy. So 500 J is added, 2000 J heat removed.

ehild

ehild said:
300 J as final energy is wrong.
When compressing, work is done on the gas, increasing the internal energy. So 500 J is added, 2000 J heat removed.

ehild

1800(Initial Energy) + 500 - 2000 = 300 J

Am I missing something or does the thermal energy also play a factor.

The work done and the heat removed changes the thermal energy, which is 5/2 RT for one mole of a diatomic molecule. ehild

ehild said:
The work done and the heat removed changes the thermal energy, which is 5/2 RT for one mole of a diatomic molecule.

ehild

I took that approach and my answer was still wrong.

Could you show your work in detail?

ehild

ehild said:
Could you show your work in detail?

ehild

3000 J(thermal energyinitial) + 500 J - 2000 = E thermalfinal = 5/3(1/2)mv2

3000 J was the initial thermal energy . It decreased by 1500 J, the final thermal energy is 1500 J. The thermal energy is 5/3 (1/2 mv^2). So how much is 1/2 mv^2, the translational kinetic energy? How much is v, the rms speed? ehild

## 1. What is the formula for calculating the rms speed of hydrogen molecules?

The formula for calculating the rms (root mean square) speed of hydrogen molecules is given by: vrms = √(3RT/M), where R is the gas constant, T is the temperature in Kelvin, and M is the molar mass of hydrogen gas.

## 2. How do you convert temperature from degrees Celsius to Kelvin?

To convert temperature from degrees Celsius to Kelvin, simply add 273.15 to the temperature in degrees Celsius. For example, if the temperature is 25°C, the equivalent temperature in Kelvin would be 298.15 K.

## 3. What is the value of the gas constant (R) in the formula for rms speed?

The value of the gas constant (R) depends on the units used for temperature and pressure. The most commonly used value is 0.0821 L·atm/mol·K. However, if pressure is given in units of Pa, then R = 8.314 J/mol·K.

## 4. Is the rms speed of hydrogen molecules affected by changes in pressure?

Yes, the rms speed of hydrogen molecules is affected by changes in pressure. According to the ideal gas law, pressure and volume are inversely proportional, so as pressure increases, volume decreases. This results in an increase in the rms speed of molecules.

## 5. What is the significance of calculating the rms speed of hydrogen molecules?

Calculating the rms speed of hydrogen molecules is significant because it is a measure of the average speed of molecules in a gas sample. It is also related to other important properties, such as the kinetic energy and pressure of the gas. This calculation is often used in thermodynamics and other areas of science to understand the behavior of gases.

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