What volume will 73 g of dry ammonia gas occupy at 11 degrees C and 720 mm Hg? How much air is needed to dilute the ammonia to 10 ppm ?
To determine the volume of dry ammonia gas at a given temperature and pressure, you need to use the Ideal Gas Law equation:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in L)
n = number of moles
R = gas constant (0.0821 L·atm/mol·K)
T = temperature (in Kelvin)
First, let's convert the given temperature to Kelvin:
11 degrees C + 273.15 = 284.15 K
Next, let's convert the given pressure to atm:
720 mm Hg * 1 atm / 760 mm Hg = 0.947 atm
Now, we need to calculate the number of moles of ammonia gas. To do this, we need to know the molecular weight of ammonia (NH3), which is approximately 17 grams/mol.
Number of moles = mass / molecular weight
Number of moles = 73 g / 17 g/mol = 4.29 mol
Now we can plug the values into the Ideal Gas Law equation:
PV = nRT
V = nRT / P
V = (4.29 mol) * (0.0821 L·atm/mol·K) * (284.15 K) / (0.947 atm)
Calculating this expression, the volume of dry ammonia gas is approximately 114.7 L.
Now let's move on to calculating the amount of air needed to dilute the ammonia to 10 ppm (parts per million).
To find the amount of air needed, we need to know the concentration of ammonia gas in the air. Since it's given as 10 ppm, this means there are 10 parts of ammonia for every one million parts of air.
To calculate the moles of ammonia needed at the given concentration, we can use the equation:
Moles of ammonia = concentration * (moles of air / 1 million)
The moles of air can be determined using the Ideal Gas Law:
PV = nRT
n = (PV) / (RT)
Considering the pressure of air is around 1 atm and the temperature is 11 degrees C (converted to Kelvin), we can calculate the moles of air.
n = (1 atm) * V / (0.0821 L·atm/mol·K * 284.15 K)
Now we can determine the moles of ammonia needed:
Moles of ammonia = 10 ppm * (n / 1 million)
Finally, we can convert the moles of ammonia into grams by multiplying by the molecular weight of ammonia (17 g/mol):
Mass of ammonia = Moles of ammonia * Molecular weight
Calculating this expression will give us the amount of air needed to dilute the ammonia to 10 ppm.