Dinitrogen oxide (N2 O) gas was generated
from the thermal decomposition of ammo-
nium nitrate and collected over water. The
wet gas occupied 124 mL at 21◦ C when the
atmospheric pressure was 752 Torr. What vol-
ume would the same amount of dry dinitrogen
oxide have occupied if collected at 752 Torr
and 21 ◦ C? The vapor pressure of water is
18.65 Torr at 21◦C.
Answer in units of mL
P1V1 = P2V2
P1 = (752-18.65)= ?
V1 = 124 mL
P2 = 752
V2 = solve for this.
oooh okay, i didn't know how to do an equation that involved vapor pressure. Thank you!
To find the volume of the dry dinitrogen oxide (N2O) gas, we need to correct for the vapor pressure of water at the given temperature. Here are the steps to calculate the volume:
Step 1: Calculate the partial pressure of the dry N2O gas.
The total pressure measured (Ptotal) is 752 Torr, and the vapor pressure of water (Pwater) is 18.65 Torr. Therefore, the partial pressure of the dry N2O gas (Pdry) is:
Pdry = Ptotal - Pwater
Pdry = 752 Torr - 18.65 Torr
Pdry = 733.35 Torr
Step 2: Apply the ideal gas law equation to calculate the volume of the gas.
The ideal gas law equation 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)
Since we know the pressure, temperature, and volume of the wet gas, we can use these values to find the number of moles of the wet gas (n1) as follows:
PV = n1RT
n1 = PV / RT
Step 3: Convert the number of moles of the wet gas to the number of moles of the dry gas.
Since moles are conserved when the temperature and pressure are constant, the number of moles of the wet gas (n1) is also the number of moles of the dry gas (n2).
Step 4: Use the number of moles of the dry gas to calculate its volume.
We can use the ideal gas law equation again to find the volume of the dry gas by substituting the known values:
V2 = n2RT / Pdry
Step 5: Convert the volume to mL.
Finally, convert the volume from liters to milliliters by multiplying by 1000:
V2 (in mL) = V2 (in L) x 1000
By following these step-by-step calculations, you can find the volume of the dry dinitrogen oxide gas.
To solve this problem, we need to consider the ideal gas law and Dalton's law of partial pressures.
1. Determine the partial pressure of dry dinitrogen oxide:
The total pressure is given as 752 Torr. Subtract the vapor pressure of water (18.65 Torr) to find the partial pressure of dry dinitrogen oxide:
Partial pressure of N2O = total pressure - vapor pressure of water
Partial pressure of N2O = 752 Torr - 18.65 Torr = 733.35 Torr
2. Apply the ideal gas law to find the volume of dry dinitrogen oxide:
The ideal gas law is given as PV = nRT. Here, P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
We need to convert the volume of the wet gas (124 mL) to liters and the temperature (21°C) to Kelvin:
Volume of wet gas in liters = 124 mL ÷ 1000 mL/L = 0.124 L
Temperature in Kelvin = 21°C + 273.15 = 294.15 K
3. Calculate the volume of dry dinitrogen oxide:
Using the ideal gas law, we can rearrange the formula to solve for V. Substitute the known values into the equation and solve for V:
V = (nRT) / P
Since the number of moles (n) and the gas constant (R) are constant, we can express the equation as:
V = (constant) × (temperature) / (pressure)
V = (0.124 L) × (294.15 K) / (733.35 Torr)
V = 0.049695 L or 49.695 mL (rounded to three decimal places)
Therefore, the volume that the same amount of dry dinitrogen oxide would occupy, when collected at 752 Torr and 21°C, is approximately 49.695 mL.