Gas is contained in a n 8L vessel at a temperature of 20¡ãC and a pressure of 9atm. a)Determine the number of moles of gas in the vessel. b) How many molecules are there in the vessel?
a. Use PV = nRT and solve for n. Remember T must be in kelvin.
b. Can't be done without knowing more information. If the gas is monatomic then b is the same as a.
If the gas is diatomic, then b is 1/2 a. If it is triatomic, then b is 1/3 a.
To find the number of moles of gas in the vessel, we can use the ideal gas law equation:
PV = nRT
where:
P = pressure in atmospheres (atm)
V = volume in liters (L)
n = number of moles (mol)
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature in Kelvin (K)
Now let's solve for the number of moles (n):
n = PV / RT
a) To find the number of moles of gas in the vessel:
First, we need to convert the temperature from Celsius to Kelvin. The temperature in Kelvin is obtained by adding 273.15 to the Celsius temperature.
T = 20°C + 273.15 = 293.15 K
Now, substitute the given values into the equation:
n = (9 atm) * (8 L) / (0.0821 L·atm/(mol·K)) * (293.15 K) = 28.16 mol
Therefore, there are approximately 28.16 moles of gas in the vessel.
b) To find the number of molecules in the vessel:
We can use Avogadro's number, which is 6.022 x 10^23 molecules/mol. Multiply the number of moles by Avogadro's number to get the number of molecules:
Number of molecules = (Number of moles) * (Avogadro's number)
Number of molecules = (28.16 mol) * (6.022 x 10^23 molecules/mol) = 1.694 x 10^25 molecules
Therefore, there are approximately 1.694 x 10^25 molecules in the vessel.