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?
First convert that 18.2 cm to how much pressure was exerted. The pressure of a column of water 18.2 cm high is
density x gravity x height = 1.00g/cc x 9.8 m/s^2 x 0.182m = 1.78 kPa and since the height in the buret is too high, that means the pressure on the gas inside is 1.78 kPa too much. I would convert that to mm and subtract from 748. I estimate the mm Hg for 1.78 kPa to be about 13 or so mm Hg.(You can do it another way as follows: 18.2 cm = 182 mm and 182mm/13.6 = 13.4 mm Hg)
a.
Ptotal gas = pH2O level + pH2O vapor pressure at 22C + pH2.
You know Ptotal= 748 mm
You know added pressure due to height H2O = about 13 mm (you should do that more accurately) and you can look up the vapor pressure of H2O at 22 C.
b.
Use PV = nRT to calculate n for H2 gas.
To find the pressure of hydrogen in the buret, we can make use of the hydrostatic pressure equation:
P + ρgh = Patm
Where:
P = pressure of the hydrogen gas
ρ = density of the liquid column (water)
g = acceleration due to gravity
h = height of the liquid column
Patm = atmospheric pressure
a) To find the pressure of hydrogen gas in the buret:
Given:
Water level in the buret = 18.2 cm
Density of Hg (mercury) = 13.6 g/mL
First, convert the height of the liquid column into proper units:
18.2 cm = 0.182 m
Now, calculate the pressure of the hydrogen gas:
P + (density of water x acceleration due to gravity x height) = atmospheric pressure
P + (1 g/cm³ x 9.8 m/s² x 0.182 m) = 748 torr
P + 1.79 torr ≈ 748 torr
P ≈ 748 torr - 1.79 torr
P ≈ 746.21 torr
Therefore, the pressure of hydrogen gas in the buret is approximately 746.21 torr.
b) To find the number of moles of hydrogen collected:
Given:
Volume of the gas in the buret = 38.6 mL
We can use the ideal gas law equation to calculate the number of moles:
PV = nRT
Where:
P = pressure of the gas (in atm)
V = volume of the gas (in L)
n = number of moles of gas
R = ideal gas constant (0.0821 L.atm/mol.K)
T = temperature of the gas (in Kelvin)
First, let's convert the pressure to atm:
746.21 torr/760 torr/atm = 0.981 atm
Now, convert the volume to liters (L):
38.6 mL/1000 mL/L = 0.0386 L
We also need to convert the temperature from degrees Celsius to Kelvin:
22.0 °C + 273.15 K = 295.15 K
Now, we can calculate the number of moles of hydrogen gas:
PV = nRT
(0.981 atm)(0.0386 L) = n(0.0821 L.atm/mol.K)(295.15 K)
0.0378706 = 0.0821n
n ≈ 0.461 moles
Therefore, the student collected approximately 0.461 moles of hydrogen gas.
To find the pressure of hydrogen in the buret, we need to consider the hydrostatic pressure due to the height difference between the water levels in the buret and water bath. We also need to account for the atmospheric pressure.
a) To calculate the pressure of hydrogen in the buret:
1. Convert the given height difference from cm to mL:
The density of water is 1 g/mL, so by dividing the height difference (18.2 cm) by the density, we get the volume difference.
Volume difference = 18.2 cm ÷ 1 mL/cm³ = 18.2 mL
2. Calculate the pressure difference due to the height difference:
We can use the hydrostatic pressure formula: P = ρgh, where P is pressure, ρ is density, g is acceleration due to gravity, and h is height.
Density of Hg = 13.6 g/mL
Acceleration due to gravity = 9.8 m/s² = 980 cm/s²
Pressure difference = (Density difference) × g × height difference
= (13.6 g/mL) × (980 cm/s²) × (18.2 mL)
≈ 23432.32 cm² g/s²
≈ 23432.32 dyn/cm² (since 1 g = 980 dyn)
Convert dyn/cm² to torr (1 torr = 1333.22 dyn/cm²):
Pressure difference = 23432.32 dyn/cm² ÷ 1333.22 torr/dyn/cm²
≈ 17.55 torr
3. Subtract the pressure difference from the atmospheric pressure:
Pressure of Hydrogen in the buret = Atmospheric pressure - Pressure difference
= 748 torr - 17.55 torr
≈ 730.45 torr
Therefore, the pressure of hydrogen in the buret is approximately 730.45 torr.
b) To calculate the number of moles of hydrogen collected:
1. Use the ideal gas law equation: PV = nRT
Rearranging the formula gives: n = (PV) / (RT), where n is the number of moles.
R is the ideal gas constant ≈ 0.0821 L·atm/(mol·K) or ≈ 62.3637 L·torr/(mol·K)
V is the volume of the gas = 38.6 mL
P is the pressure of hydrogen in the buret ≈ 730.45 torr
T is the temperature in Kelvin (22.0 °C = 295.15 K)
2. Convert the temperature from Celsius to Kelvin:
Kelvin temperature = Celsius temperature + 273.15
Kelvin temperature = 22.0 °C + 273.15
= 295.15 K
3. Calculate the number of moles:
n = (P × V) / (R × T)
n = (730.45 torr × 38.6 mL) / (62.3637 L·torr/(mol·K) × 295.15 K)
Make sure to convert mL to L and torr to atm:
n = (730.45 torr × 0.0386 L) / (62.3637 L·torr/(mol·K) × 295.15 K)
n ≈ 0.00516 mol
Therefore, the student collected approximately 0.00516 moles of hydrogen.