A student collected H2 gas in a buret by displacing water at 22.0 °C. The buret could not be submerged deep enough in a water bath to equalize the pressure. The water level in the buret was 18.2 cm above the water level in the water bath. The volume of the gas in the buret was determined to be 38.6 mL.
a) If the atmosphere pressure was 748 torr, what is the pressure of the Hydrogen in the buret? (Density of Hg is 13.6 g/mL)
b) How many moles of Hydrogen did the student collect?
See your post above.
To find the pressure of hydrogen in the buret, we need to consider the relationship between the gas pressure and the difference in the levels of the liquid columns in the buret and the water bath. We can use the hydrostatic pressure equation:
P1 + ρgh1 = P2 + ρgh2
Where:
P1 is the atmospheric pressure
P2 is the pressure of the hydrogen gas
ρ is the density of the liquid (in this case, water)
g is the acceleration due to gravity
h1 is the height of the water column in the buret
h2 is the height of the water column in the water bath
a) To find the pressure of the hydrogen gas (P2), we need to rearrange the equation:
P2 = P1 + ρgh1 - ρgh2
First, let's convert the height of the water column in the buret to pressure using the density of mercury (Hg) and the conversion formula for pressure:
1 cm Hg = 13.6 g/mL
1 mL Hg = 13.6 g
The height of the water column in the buret (h1) is 18.2 cm. To convert it to pressure:
h1 (in mL) = 18.2 mL
h1 (in g) = 18.2 mL x 13.6 g/mL = 247.52 g
h1 (in cm Hg) = 247.52 g / 13.6 g/mL = 18.2 cm Hg
Now, let's calculate the pressure of the hydrogen gas (P2):
P2 = 748 torr + 18.2 cm Hg - 0 cm Hg (as the water level in the water bath is the reference level)
P2 = 748 torr + 18.2 cm Hg
Therefore, the pressure of the hydrogen gas in the buret is 748 torr + 18.2 cm Hg.
b) To find the number of moles of hydrogen, we need to use the ideal gas law equation:
PV = nRT
Where:
P is the pressure of the gas
V is the volume of the gas
n is the number of moles of the gas
R is the ideal gas constant (0.0821 L x atm / mol x K)
T is the temperature in Kelvin (22.0 °C = 22.0 + 273.15 K)
Rearranging the equation:
n = PV / RT
First, convert the pressure of the hydrogen to atm:
1 torr = 1/760 atm
P2 (in atm) = (748 torr + 18.2 cm Hg) / 760 torr/atm
Now, we can calculate the number of moles of hydrogen:
n = (P2 in atm) x (V in L) / (R in L x atm/mol x K) x (T in K)
Make sure to convert the volume of the gas to liters by dividing 38.6 mL by 1000.
n = (P2 in atm) x (38.6 mL / 1000 mL) / (0.0821 L x atm/mol x K) x (22.0 + 273.15 K)
After performing the calculation, you will get the number of moles of hydrogen the student collected.