Can someone just work me through how to do this one problem? I should be OK on the rest then.
Calculate the rms speeds of N2 molecules at 23 degrees C and at 125 degrees C. Sketch the approximate curves of the molecular speed distributions of N2 at 25 degrees C and 125 degrees C.
i know the equation is u= sq root 3RT/Mm but I don't seem to get the right answer.
My work:
At 25 degrees C
u= sq rt. (3 * 8.31 * 298)/(2.80*10^-3km/mol)
u= 16.3 m/s^2
At 125 degrees C
u= sq root (3*8.31*398)/(2.80*10^-3km/mol)
u= 18.8 m/s^2
those answers are wrong. and i don't know how to do the graph
I don't know where the m (the small m) came from. I have
urms = sqrt(3RT/M)
You have 3 and R correct in the above equation. The original problem stated 23 degrees but you substituted 298 instead of 296 so you need to check and substitute the correct T. Finally, M is the molar mass in kg, which for N2 is about 0.028 kg but that is 28.0 x 10^-3 instead of the number you have. That's probably the error. Try that and see how it works. I don't know what the question is asking about the graph.
Sure, I can help you with that problem!
To calculate the root mean square (rms) speed of N2 molecules at different temperatures, you would use the equation u = √(3RT/Mm), where:
- u is the rms speed in m/s
- R is the ideal gas constant (8.314 J/(mol·K) or 0.0821 L·atm/(mol·K))
- T is the temperature in Kelvin (K)
- Mm is the molar mass of the gas molecule in kg/mol
Let's first convert the given temperatures from degrees Celsius (°C) to Kelvin (K). To do this, you simply add 273 to the °C value.
For the first part of the question, the temperature is 23 °C. Simply add 273 to it:
23 °C + 273 = 296 K
For the second part, the temperature is 125 °C:
125 °C + 273 = 398 K
Now, we can plug the values into the equation for u to calculate the rms speeds.
Step 1: Calculate the rms speed at 23 °C (296 K):
u = √(3RT/Mm)
= √(3 * 8.314 * 296 / Mm)
= √(7410.672/Mm)
Step 2: Calculate the rms speed at 125 °C (398 K):
u = √(3RT/Mm)
= √(3 * 8.314 * 398 / Mm)
= √(9947.052/Mm)
To calculate the numerical value, we need the molar mass of N2. The molar mass of N2 is approximately 28 g/mol or 0.028 kg/mol.
Step 3: Plug in the known values and calculate the rms speeds:
At 23 °C (296 K):
u = √(7410.672/0.028)
≈ √(264738.2857)
≈ 514.5 m/s
At 125 °C (398 K):
u = √(9947.052/0.028)
≈ √(355251.8571)
≈ 595.9 m/s
Therefore, the rms speed of N2 molecules at 23 °C is approximately 514.5 m/s, and at 125 °C is approximately 595.9 m/s.
Regarding the second part of the question, to sketch the approximate curves of the molecular speed distributions of N2 at 25 °C and 125 °C, you can use a Maxwell-Boltzmann distribution. The distribution curve is bell-shaped, with the peak representing the most probable molecular speed. As the temperature increases, the curve shifts to the right and becomes broader, indicating a wider distribution of speeds.
I hope this explanation helps you understand the steps involved in solving the problem! Let me know if you have any further questions.