Each of four identical tires of a car is filled with a different gas. Gas pressure in each tire is 3.0 atm at 25oC. One tire contains neon, another – argon, the 3rd one has krypton, and the last one has unknown gas. How many molecules are there in each tire?
So far, I have used PV=nRT. I set V=1. I found that n = .1226 moles. I multiplied that by avogadros number and got
7.38 * 10 ^ 22 molecules. Is this correct?
How do you know V = 1? If you set V = 2 (or 3, or 4 or 5) will that change the number of molecules.
n = PV/RT
You do not know the volumes of the tires except that they are all the same. "V = 1" (an arbitrary unit of volume) cannot give you a specific number of moles or number of molecules. However how do the numbers of molecules for each gas compare to each other?
To determine the number of molecules in each tire, you correctly started by using the ideal gas law equation, PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.
Given:
Pressure (P) = 3.0 atm
Temperature (T) = 25°C or 298 K
Volume (V) = 1 tire
First, convert the temperature from Celsius to Kelvin by adding 273:
T = 25°C + 273 = 298 K
Next, rearrange the ideal gas law equation to solve for the number of moles (n):
n = PV / RT
Plugging in the values:
n = (3.0 atm) * (1 tire) / [(0.0821 L·atm/mol·K) * (298 K)]
n ≈ 0.1226 moles
Now, to find the number of molecules in each tire, you can use Avogadro's number (6.022 x 10^23 molecules/mol). Multiply the number of moles by Avogadro's number:
Number of molecules = (0.1226 moles) * (6.022 x 10^23 molecules/mol)
Number of molecules ≈ 7.38 x 10^22 molecules
So, you correctly calculated that there are approximately 7.38 x 10^22 molecules in each tire. Therefore, your answer is correct.