calculate the volume occupied by 10^22 molecules of a gas 300 k and 760 mm pressure.
please help me please...................
To calculate the volume occupied by 10^22 molecules of a gas at a given temperature and pressure, we can use the ideal gas law equation which is:
PV = nRT
where:
P is the pressure of the gas
V is the volume occupied by the gas
n is the number of moles of the gas
R is the ideal gas constant (0.0821 L·atm/mol·K)
T is the temperature in Kelvin
First, we need to convert the given pressure from mmHg to atm:
760 mmHg = 760/760 = 1 atm
Next, we need to calculate the number of moles of the gas. Since we are given the number of gas molecules, we can use Avogadro's number (6.022 x 10^23 molecules/mol) to convert it to moles:
n = (10^22 molecules) / (6.022 x 10^23 molecules/mol)
Now, from the question, the temperature is given as 300 K.
We can substitute the values into the ideal gas law equation:
(1 atm) * V = [(10^22) / (6.022 x 10^23)] * (0.0821 L·atm/mol·K) * (300 K)
Simplifying the equation:
V = [(10^22) / (6.022 x 10^23)] * (0.0821 L·atm/mol·K) * (300 K) / (1 atm)
Now, let's calculate the volume:
V = (10^22) * (0.0821) * (300) / (6.022 x 10^23)
V ≈ 13.625 L
Therefore, the volume occupied by 10^22 molecules of the gas at 300 K and 760 mmHg is approximately 13.625 liters.
To calculate the volume occupied by a given number of molecules of a gas, we can use the ideal gas law equation, which states:
PV = nRT
Where:
P = pressure of the gas
V = volume of the gas
n = number of moles of the gas
R = ideal gas constant
T = temperature in Kelvin
To solve for volume, rearrange the equation:
V = (nRT) / P
Given:
P = 760 mmHg (pressure)
T = 300 K (temperature)
n = 10^22 molecules
First, we need to convert the pressure from mmHg to atm (standard unit for pressure in the ideal gas law equation).
1 atm = 760 mmHg
So, the pressure in atm = 760 mmHg / 760 mmHg/atm = 1 atm
Next, convert the number of molecules to moles. We know that 1 mole of any substance contains Avogadro's number of molecules, which is approximately 6.022 x 10^23.
n = 10^22 molecules / (6.022 x 10^23 molecules/mol) = 1.66 x 10^-2 mol
Now we have all the values we need to calculate the volume.
V = (nRT) / P
= (1.66 x 10^-2 mol) x (0.0821 L·atm/mol·K) x (300 K) / (1 atm)
≈ 0.403 L
Therefore, the volume occupied by 10^22 molecules of the gas at 300 K and 760 mmHg pressure is approximately 0.403 L.
408.9 cm3
Use PV = nRT
n = 1E22/6.02E23
Remember to convert 760 mm to atm (it is 1 atm)
Remember T must be in kelvin.l