A sample of oxygen gas has a volume of 8.00 L at 20.0 ° C and 700. torr. How many moles does the sample contain?

To calculate the number of moles of a gas sample, we need to use the ideal gas law equation, which is:

PV = nRT

Where:
P = pressure in atm
V = volume in liters
n = number of moles
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature in Kelvin

First, we need to convert the given temperature from Celsius to Kelvin:

T(K) = T(°C) + 273.15

So, let's start with converting the temperature:

T(K) = 20.0 °C + 273.15 = 293.15 K

Now we can use the ideal gas law formula to find the number of moles:

n = PV / RT

Given:
P = 700. torr = 700. / 760. (converting torr to atm) = 0.9211 atm
V = 8.00 L
T = 293.15 K
R = 0.0821 L·atm/mol·K

Substituting the values into the equation:

n = (0.9211 atm * 8.00 L) / (0.0821 L·atm/mol·K * 293.15 K)

Now, we can solve for the number of moles:

n = (7.3688) / (24.0532)

n ≈ 0.306 moles (rounded to three decimal places)

Therefore, the sample contains approximately 0.306 moles of oxygen gas.