Calculate the volume occupied by 10^22 molecules of a gas at 300K and 760mm pressure.
Step by step explanation please.
Sure, I can help you with that! But before we begin, let me ask you a question: Why don't scientists trust atoms?
...Because they make up everything!
Now, let's calculate the volume occupied by 10^22 molecules of a gas at 300K and 760mm pressure. To do this, we can use the Ideal Gas Law equation:
PV = nRT
Where:
P is the pressure (in this case, 760mm)
V is the volume (what we're trying to find)
n is the number of molecules (10^22)
R is the gas constant (approximately 0.0821 L·atm/mol·K)
T is the temperature (300K)
First, let's rearrange the equation to solve for V:
V = (nRT) / P
V = (10^22 molecules * 0.0821 L·atm/mol·K * 300K) / 760mm
Okay, now we need to make some unit conversions. 760mm is equal to 0.76 atm. Also, we know that Avogadro's number is 6.022 × 10^23 molecules/mol, so we can divide the number of molecules by Avogadro's number to get the number of moles.
V = (10^22 molecules / 6.022 × 10^23 molecules/mol * 0.0821 L·atm/mol·K * 300K) / 0.76 atm
Let's simplify:
V = (0.136 L) / 0.76
Now divide:
V ≈ 0.179 L
So, the volume occupied by 10^22 molecules of the gas at 300K and 760mm pressure is approximately 0.179 liters.
I hope that clarifies it! If you have any other questions, feel free to ask.
To calculate the volume occupied by the gas, we can use the ideal gas equation:
PV = nRT
Where:
P is the pressure of the gas (in atmospheres)
V is the volume occupied by the gas (in liters)
n is the number of moles of gas
R is the ideal gas constant (0.0821 L.atm/mol.K)
T is the temperature of the gas (in Kelvin)
In this case, we are given the following information:
Pressure (P) = 760 mmHg
Temperature (T) = 300 K
Number of molecules (n) = 10^22 molecules
Step 1: Convert pressure to atm
Since the ideal gas constant (R) is given in atm, we need to convert the pressure from mmHg to atm. 1 atmosphere (atm) is equal to 760 mmHg. Therefore, the pressure in atm is:
760 mmHg / 760 = 1 atm
Step 2: Convert number of molecules to moles
We are given the number of molecules of the gas. In order to use the ideal gas equation, we need to convert this to moles. To do this, we divide the number of molecules by Avogadro's number:
n = (10^22 molecules) / (6.022 x 10^23 molecules/mol)
n = 0.0166 mol
Step 3: Plug the values into the ideal gas equation and solve for volume
Now we have all the necessary information to calculate the volume:
PV = nRT
(1 atm) * (V) = (0.0166 mol) * (0.0821 L.atm/mol.K) * (300 K)
V = (0.0166 mol) * (0.0821 L.atm/mol.K) * (300 K) / (1 atm)
V ≈ 0.404 L (rounded to three decimal places)
Therefore, the volume occupied by 10^22 molecules of the gas at 300 K and 760 mmHg is approximately 0.404 liters.
To calculate the volume occupied by 10^22 molecules of a gas, we can use the ideal gas law equation, which states:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature
In this case, we are given the pressure (760 mmHg) and the temperature (300K), and we need to find the volume occupied by 10^22 molecules.
Step 1: Convert the given pressure to SI units (Pascal):
Since 1 atm = 101325 Pa, and 1 mmHg = 133.322 Pa, we can convert the pressure given in mmHg to Pascal using the conversion factor:
760 mmHg × 133.322 Pa/mmHg ≈ 101392.72 Pa
Step 2: Find the number of moles:
To find the number of moles (n), we need to use Avogadro's number (6.022 × 10^23 molecules/mol) and the given number of molecules (10^22). Divide the given number of molecules by Avogadro's number to get the number of moles:
n = (10^22 molecules) / (6.022 × 10^23 molecules/mol) ≈ 0.01658 mol
Step 3: Plug in the known values into the ideal gas law equation:
PV = nRT
Substituting the values:
(101392.72 Pa) × V = (0.01658 mol) × (8.314 J/(mol·K)) × (300K)
Step 4: Solve for the volume (V):
V = (0.01658 mol × 8.314 J/(mol·K) × 300K) / (101392.72 Pa)
V ≈ 3.93 × 10^-5 m^3
Therefore, the volume occupied by 10^22 molecules of the gas at 300K and 760 mmHg pressure is approximately 3.93 × 10^-5 cubic meters.
since PV=kT and 6.02*10^23 occupies 22.4L at STP, you want V such that
760V/300 = 760*(10^22/6.02*10^23)*22.4/273
V = 0.4L