Calculate the volume of a gas @ 20 degrees C and 640 mm Hg if it's volume is 1500 mL when collected @ STP.
To calculate the volume of a gas at a given temperature and pressure, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in atmospheres)
V = volume (in liters)
n = number of moles of gas
R = ideal gas constant (0.0821 L•atm/mol•K)
T = temperature (in Kelvin)
First, let's convert the given values to the correct units. We have a pressure of 640 mm Hg, which can be converted to atmospheres (atm) by dividing by 760 (since 760 mm Hg is equivalent to 1 atm):
Pressure (P) = 640 mm Hg / 760 mm Hg/atm ≈ 0.8421 atm
Next, we need to convert the temperature from degrees Celsius to Kelvin. The Kelvin scale is obtained by adding 273.15 to the Celsius temperature:
Temperature (T) = 20 + 273.15 = 293.15 K
Now we have the pressure (P) and temperature (T) values that we need. To find the volume (V), we need to determine the number of moles of gas (n) first:
To calculate the number of moles (n), we can use the ideal gas law equation again, rearranged to solve for n:
PV = nRT
n = PV / RT
Using the values we have:
n = (0.8421 atm) x (1500 mL / 1000 mL/L) / (0.0821 L•atm/mol•K) x (293.15 K)
Note that we converted the volume from milliliters (mL) to liters (L) by dividing by 1000.
Now let's calculate n:
n = (0.8421 atm) x (1.5 L) / (0.0821 L•atm/mol•K) x (293.15 K)
n ≈ 0.0586 moles
Now that we have the number of moles (n), we can find the volume (V) of the gas at 20 degrees Celsius and 640 mm Hg using the ideal gas law equation:
PV = nRT
V = (nRT) / P
V = (0.0586 mol x 0.0821 L•atm/mol•K x 293.15 K) / 0.8421 atm
V ≈ 16.96 L
Therefore, the volume of the gas at 20 degrees Celsius and 640 mm Hg is approximately 16.96 liters.