Consider a 790-mL container at 21 °C in which the pressure of argon is 1.98x106 Pa.
a) What mass of argon (in g) is present in this container?
b) How many molecules is this?
a) Use PV = nRT, solve for n
n = grams/molar mass, solve for grams.
b) 1 mole contains 6.022 x 10^23 molecules. How many moles do you have?
WHich (R) do I have to use
To find the mass of argon present in the container, you can use the ideal gas law equation:
PV = nRT
P = pressure of the gas (in Pa)
V = volume of the container (in m^3)
n = number of moles of gas
R = ideal gas constant (8.314 J/(mol·K))
T = temperature of the gas (in Kelvin)
First, let's convert the temperature from Celsius to Kelvin:
T = 21 °C + 273.15 = 294.15 K
Next, let's convert the volume of the container from milliliters to cubic meters:
V = 790 mL = 790/1000 = 0.79 L = 0.79/1000 = 0.00079 m^3
Now, we can rearrange the ideal gas law equation to solve for the number of moles of gas (n):
n = PV / RT
Substituting the given values:
n = (1.98x10^6 Pa) * (0.00079 m^3) / ((8.314 J/(mol·K)) * (294.15 K))
Calculating this, we find:
n ≈ 0.094 moles
To find the mass of argon, we need to use the molar mass of argon which is approximately 39.95 g/mol. We can calculate the mass using the formula:
Mass (g) = number of moles of gas * molar mass of gas
Substituting the values:
Mass (g) = 0.094 moles * 39.95 g/mol
Calculating this, we find:
Mass (g) ≈ 3.76 g
Therefore, the mass of argon present in the container is approximately 3.76 grams.
Now, to find the number of molecules of argon, we can use Avogadro's number (6.022x10^23 molecules/mol). Multiplying the number of moles by Avogadro's number will give us the number of molecules:
Number of molecules = number of moles * Avogadro's number
Substituting the values:
Number of molecules ≈ 0.094 moles * (6.022x10^23 molecules/mol)
Calculating this, we find:
Number of molecules ≈ 5.659 x 10^22 molecules
Therefore, the number of molecules of argon present in the container is approximately 5.659 x 10^22 molecules.