Ideal gas and Thermo question

In summary, to solve this problem, we use the equations d(PV) = d(nRT) and dH = dE + d(PV) and rearrange the ideal gas law to solve for dP. Then, we plug in the given values for n, R, dT, and V to calculate d(PV). Finally, we use the equation dH = dE + d(PV) to solve for dH by plugging in the given value for dE and the calculated value for d(PV).
  • #1
legge
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Homework Statement



A chemical reaction is a gas mixture at 500 degrees C decreases the number of moles of gas, which is assumed to behave ideally, by 34.7%. If the internal energy change is 23.8 kJ, what is the value of dH.

Homework Equations



Not sure if they are complete relevant but...
d(PV) = d(nRT)
dH = dE + d(PV)

The Attempt at a Solution



So...what I was thinking of doing was using dH = dE + dPV.

We are given dE. To find d(PV), I was thinking of using d(nRT), because it tells us the change in moles. I feel that I'm close, but I know that you can't just put in the change in percent for the change in moles.
 
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  • #2


Thank you for your post. You are on the right track with using the equations d(PV) = d(nRT) and dH = dE + d(PV) to solve this problem. However, there are a few things to consider in order to arrive at the correct answer.

First, let's rewrite the given information in a clearer form. We know that the gas mixture is at a temperature of 500 degrees C and that it decreases the number of moles of gas by 34.7%. We also know that the internal energy change (dE) is 23.8 kJ. Using the ideal gas law, we can rewrite the equation d(PV) = d(nRT) as d(PV) = nRdT, where n is the number of moles of gas and dT is the change in temperature.

Now, we need to determine the value of d(PV) in order to solve for dH. Since we are given the change in moles (34.7%), we can use this value to calculate the change in pressure (dP). This can be done by rearranging the ideal gas law to solve for dP: dP = -nRdT/V, where V is the volume of the gas mixture.

Next, we can substitute this value for dP into the equation d(PV) = nRdT, giving us d(PV) = -nRdT^2/V. Now, we can plug in the given values for n, R, dT, and V to solve for d(PV).

Once we have the value for d(PV), we can use the equation dH = dE + d(PV) to calculate dH. Plug in the given value for dE and the calculated value for d(PV) to arrive at the final answer for dH.

I hope this helps and clarifies the steps needed to solve this problem. Keep up the good work in your studies!

Scientist
 

What is an ideal gas?

An ideal gas is a theoretical gas that follows the gas laws (Boyle's Law, Charles's Law, and Avogadro's Law) at all temperatures and pressures. In an ideal gas, the particles have no volume and there are no intermolecular forces between them.

What are the assumptions of an ideal gas?

The assumptions of an ideal gas are:

  • The gas particles have no volume.
  • The gas particles do not interact with each other.
  • The gas particles are in constant, random motion.
  • The collisions between gas particles and the container walls are elastic.
  • The average kinetic energy of the gas particles is directly proportional to the temperature.

What is the difference between an ideal gas and a real gas?

An ideal gas is a theoretical gas that follows the gas laws perfectly, while a real gas does not. Real gases have volume and intermolecular forces that affect their behavior. At high pressures or low temperatures, real gases deviate from ideal gas behavior.

How does temperature affect the behavior of an ideal gas?

According to Charles's Law, the volume of an ideal gas is directly proportional to its temperature, when pressure and number of particles are constant. This means that as temperature increases, the volume of the gas also increases. Additionally, the average kinetic energy of the gas particles increases with temperature, leading to higher pressure and a greater tendency for the gas to expand.

What is thermodynamics and how does it relate to ideal gases?

Thermodynamics is the study of the relationships between heat, work, energy, and temperature. Ideal gases are often used in thermodynamics because they follow simple and predictable relationships between these variables, making calculations easier. The ideal gas law, PV = nRT, is also an important equation in thermodynamics that relates pressure, volume, temperature, and number of moles of an ideal gas.

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