A sample of H2 is collected by displacing 145 mL of water. The pressures of the gas and the atmosphere are equalized. The atmospheric pressure is 745 mmHg. The temperature of the water and gas are identical at 26 degrees C. How many moles of H2 have been evolved?
To determine the number of moles of H2 evolved, we can use the combined gas law and the ideal gas law. First, let's start by calculating the partial pressure of H2.
Since the water and gas are at the same temperature and the atmospheric pressure is equal to the gas pressure, we can use the partial pressure of H2 (P_H2) and the total pressure (P_total = atmospheric pressure) to calculate the moles of H2 evolved.
Step 1: Convert the given atmospheric pressure from mmHg to atm.
1 atm = 760 mmHg
Atmospheric pressure (P_total) = 745 mmHg / 760 mmHg/atm
Step 2: Calculate the partial pressure of H2 using the total pressure.
P_H2 = P_total
Step 3: Convert the temperature from Celsius to Kelvin.
T (in Kelvin) = 26 degrees C + 273 = 299 K
Step 4: Apply the ideal gas law formula to calculate the moles of H2.
PV = nRT
R = ideal gas constant = 0.0821 L.atm/(mol.K)
V = volume of H2 evolved (given as 145 mL = 0.145 L)
n = number of moles of H2 (to be determined)
T = temperature in Kelvin (299 K)
Rearranging the formula, we get:
n = PV / RT
Substituting the values:
n = (P_H2 x V) / (R x T)
Now, let's plug in the values and calculate the number of moles of H2.
n = (P_H2 x V) / (R x T)
n = (P_total x V) / (R x T)
n = (0.745 atm x 0.145 L) / (0.0821 L.atm/(mol.K) x 299 K)
To find the number of moles of H2 evolved, we can use the ideal gas law equation:
PV = nRT
Where:
P is the pressure of the gas (in atm)
V is the volume of the gas (in liters)
n is the number of moles of gas
R is the ideal gas constant (0.0821 L·atm/mol·K)
T is the temperature of the gas (in Kelvin)
First, let's convert the pressure from mmHg to atm:
745 mmHg * (1 atm / 760 mmHg) = 0.980 atm
Next, let's convert the volume from mL to liters:
145 mL * (1 L / 1000 mL) = 0.145 L
Now let's convert the temperature from Celsius to Kelvin:
26 degrees C = 26 + 273.15 K = 299.15 K
Plugging the values into the ideal gas law equation:
0.980 atm * 0.145 L = n * 0.0821 L·atm/mol·K * 299.15 K
Simplifying:
0.1421 = n * 24.583715
Dividing both sides by 24.583715:
n = 0.005785056 moles
Therefore, approximately 0.006 moles of H2 have been evolved.
First, get the water vapor pressure at 26C. Subtract that water partial pressure from the pressure in the tube, and you have the pressure of H2, you are given the temp, and the volume.
use n=PV/RT to get moles.