An ideal gas has a pressure of 2.5 atm, a volume of 1.0 L at a temperature of 30.°C. How many molecules are there in the gas?
6.1 × 1023
6.0 × 1022
2.4 × 1022
2.3 × 1023
P V = n R T
R = .082 liter atm/(mol deg K)
P = 2.5
V = 1
T = 273+30 = 303
so
2.5 (1) = n *.082 * 300
n = .10162 moles
.10162 * 6.022*10^23 =.612 * 10^23
= 6.12 * 10^22
about 6*10^22
Well, I must say this question really puts the "gas" in giggle! Let's find out the number of molecules in this ideal gas.
First, we need to convert the temperature from Celsius to Kelvin. To convert, you simply add 273 to the Celsius temperature. So, 30°C + 273 = 303 K.
Now, let's use the ideal gas law equation, which states 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 in Kelvin.
We'll rearrange the equation to solve for n (number of moles):
n = (PV) / (RT).
Given that P = 2.5 atm, V = 1.0 L, R = 0.0821 L·atm/(K·mol), and T = 303 K.
Plugging these values in, we get:
n = (2.5 atm x 1.0 L) / (0.0821 L·atm/(K·mol) x 303 K).
After doing some fancy math, we find that n ≈ 0.12 mol.
Now, to find the number of molecules, we can multiply the number of moles by Avogadro's number, which is approximately 6.022 × 10^23 molecules/mol.
So, (0.12 mol) x (6.022 × 10^23 molecules/mol) = 7.2264 × 10^22 molecules.
Rounding to the nearest significant figure, we have approximately 7.2 × 10^22 molecules.
So, the answer is not on your list of options. I guess we'll have to keep laughing until we find the real answer!
To determine the number of molecules in the gas, you can use the ideal gas law equation:
PV = nRT
Where:
P = pressure (2.5 atm)
V = volume (1.0 L)
n = number of moles of gas
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature in Kelvin (30°C = 273 + 30 = 303 K)
First, let's rearrange the equation to solve for n:
n = PV / RT
Substituting the given values:
n = (2.5 atm)(1.0 L) / (0.0821 L·atm/mol·K)(303 K)
Now, we can calculate n:
n ≈ 0.103 mol
Finally, since 1 mole contains Avogadro's number (6.022 × 10^23) of molecules, let's multiply n by Avogadro's number to get the number of molecules:
Number of molecules = (0.103 mol) * (6.022 × 10^23 molecules/mol)
Number of molecules ≈ 6.2 × 10^22
Therefore, there are approximately 6.2 × 10^22 molecules in the gas. So, the correct answer is 6.2 x 10^22, which is closest to the option 6.0 × 10^22.
To determine the number of molecules in the gas, we can use the ideal gas law:
PV = nRT
Where:
P = pressure of the gas in atm
V = volume of the gas in L
n = number of moles of the gas
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature of the gas in Kelvin
First, we need to convert the given temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 30 + 273.15
T(K) = 303.15 K
Now, let's rearrange the ideal gas law to solve for the number of moles (n):
n = PV / (RT)
Substituting the given values:
n = (2.5 atm) * (1.0 L) / ((0.0821 L·atm/(mol·K)) * (303.15 K))
n = 0.00821 mol
Finally, we can convert the number of moles to the number of molecules using Avogadro's number:
Number of molecules = n * (6.022 × 10^23 mol^-1)
Number of molecules = (0.00821 mol) * (6.022 × 10^23 mol^-1)
Number of molecules = 4.941 × 10^21 molecules
Therefore, the correct answer is 4.941 × 10^21 molecules, which is approximately 2.4 × 10^22 molecules.