Hi- we were given this question and I have no clue how to figure it out...please help!
Which gas molecules have the greatest average speed at STP?
[a] SO2( sulfur dioxide)
[b] NH3( ammonia)
[c] O2( oxygen)
[d] N20 (Dinitrogen oxide)
Ok, at stp, that means they all have the same average kinetic energy. But KE= 1/2 mv^2, so the one with the greatest speed must have the least mass.
thank you so much
jug
b] ammonia
ammonia
You're welcome! I'll help you understand how to figure out which gas molecules have the greatest average speed at STP.
To begin, let's recall what STP means. STP stands for Standard Temperature and Pressure. At STP, the temperature is 273.15 Kelvin (0 degrees Celsius) and the pressure is 1 atmosphere (atm).
Now, let's consider the concept of kinetic energy (KE) which is directly related to the average speed of gas molecules. The kinetic energy of a gas molecule can be calculated using the formula KE = 1/2 * mass * velocity^2.
Since we are comparing gas molecules at STP with the same average kinetic energy, we can assume their kinetic energies are equal. Therefore, we can rewrite the formula as:
1/2 * mass1 * velocity1^2 = 1/2 * mass2 * velocity2^2
Now, as you already mentioned, KE is proportional to the square of the velocity. So, if the kinetic energy is the same for all gases, we can infer that the gas molecule with the greatest average speed has the least mass.
Let's analyze the given options:
[a] SO2 (sulfur dioxide) - Sulfur dioxide has a molar mass of 64.06 g/mol.
[b] NH3 (ammonia) - Ammonia has a molar mass of 17.03 g/mol.
[c] O2 (oxygen) - Oxygen has a molar mass of 32.00 g/mol.
[d] N2O (dinitrogen oxide) - Dinitrogen oxide has a molar mass of 44.01 g/mol.
Comparing the molar masses, we can see that the gas molecule with the least mass is NH3 (ammonia) since it has the smallest molar mass.
Therefore, the gas molecule with the greatest average speed at STP is NH3 (ammonia), option [b].
I hope this explanation helps! If you have any further questions, feel free to ask.