calculate the number of moles of gaseous N2 contained in a sample of 300 ml of gas saturated with water vapour at 25 degree celcius and 95 kPa.
Well, calculating the number of moles of gas can be a bit dry, so let's spice it up with a little joke, shall we?
Why did the mole bring a calculator to the party?
Because it loved to convert moles to particles and solve for n!
Now, let's get down to business. To calculate the number of moles of N2, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in Pascal)
V = volume (in m^3)
n = number of moles
R = ideal gas constant (8.314 J/(mol·K))
T = temperature (in Kelvin)
First, let's convert the given values to the appropriate units. We can convert 300 mL to 0.3 L, 95 kPa to 95000 Pa, and 25 degrees Celsius to 298 K.
Now, let's plug these values in:
(95000 Pa) * (0.3 L) = n * (8.314 J/(mol·K)) * (298 K)
Solving for n, we find:
n = (95000 Pa * 0.3 L) / (8.314 J/(mol·K) * 298 K)
After crunching the numbers, we get n ≈ 11.167 moles.
So, to answer your question, there are approximately 11.167 moles of gaseous N2 in that sample. I hope this answer doesn't "mole" you to death!
To calculate the number of moles of gaseous N2, we will use the ideal gas law equation:
PV = nRT
Where:
P = Pressure
V = Volume
n = Number of moles
R = Ideal gas constant
T = Temperature
First, we need to calculate the partial pressure of N2 gas in the sample. The total pressure (P) is given as 95 kPa, and the partial pressure of water vapor (P_water) can be determined using the vapor pressure of water at 25°C. We assume that the partial pressure of N2 (P_N2) is the difference between the total pressure and the vapor pressure of water.
The vapor pressure of water at 25°C is approximately 3.17 kPa.
P_water = 3.17 kPa
P_N2 = P - P_water
P_N2 = 95 kPa - 3.17 kPa
P_N2 = 91.83 kPa
Now, we can rearrange the ideal gas law equation to solve for the number of moles:
n = PV / RT
Rearranging the equation:
n = (P_N2 * V) / (R * T)
Substituting the given values:
P_N2 = 91.83 kPa
V = 300 ml = 0.3 L (converted from milliliters to liters)
R = 8.314 J/(mol·K) (ideal gas constant)
T = 25°C = 298 K (converted from Celsius to Kelvin)
n = (91.83 kPa * 0.3 L) / (8.314 J/(mol·K) * 298 K)
Now, let's calculate the number of moles.
n = (27.549 L·kPa) / (8.314 J/(mol·K) * 298 K)
n = 27.549 L·kPa / (2470.572 J/mol)
n ≈ 0.01115 mol
Therefore, the number of moles of gaseous N2 in the sample is approximately 0.01115 mol.
To calculate the number of moles of gaseous N2, you will need to use the ideal gas law equation:
PV = nRT
where:
P = pressure (in kilopascals, kPa)
V = volume (in liters, L)
n = number of moles of gas
R = ideal gas constant (0.0821 L·atm/(mol·K) or 8.314 J/(mol·K))
T = temperature (in Kelvin, K)
First, convert the given volume from milliliters (ml) to liters (L):
300 ml = 300/1000 L = 0.3 L
Next, convert the given temperature from degrees Celsius to Kelvin:
T = 25°C + 273.15 = 298.15 K
Now, you have the values you need to solve the equation. However, there's a slight complication because the gas is saturated with water vapor.
When a gas is saturated with water vapor, the vapor pressure of water needs to be considered. At 25°C, the vapor pressure of water is approximately 3.17 kPa. Therefore, the effective pressure of N2 gas will be:
Effective Pressure = Total Pressure - Vapor Pressure
Effective Pressure = 95 kPa - 3.17 kPa = 91.83 kPa
Now, substitute the values into the equation:
PV = nRT
(91.83 kPa) * (0.3 L) = n * (8.314 J/(mol·K)) * (298.15 K)
Solve for n:
n = (91.83 kPa * 0.3 L) / (8.314 J/(mol·K) * 298.15 K)
Now, calculate the number of moles of N2:
n = 0.01124 moles (rounded to five decimal places)
Therefore, there are approximately 0.01124 moles of gaseous N2 in the given sample.