How much acetone liquid (in mls) is required to produce a vapor concentration of
200 ppm (parts per million) by volume in a room of dimensions 3 x 4 x 10
meters? The temperature is 25oC and the pressure is 1 atm. The following
physical property data are available for acetone:
Molecular weight: 58
Specific gravity: 0.781
To calculate the volume of acetone liquid required to produce a vapor concentration of 200 ppm in a room, we need to use the following steps:
Step 1: Calculate the volume of the room
The room dimensions are given as 3 x 4 x 10 meters, so the volume of the room can be calculated by multiplying the dimensions together:
Volume = Length x Width x Height
= 3 meters x 4 meters x 10 meters
= 120 cubic meters
Step 2: Convert the volume of the room to liters
Since we are dealing with the volume of a liquid, it is more convenient to work with liters instead of cubic meters. We know that 1 cubic meter is equal to 1000 liters, so:
Volume (in liters) = Volume (in cubic meters) x 1000
= 120 cubic meters x 1000
= 120000 liters
Step 3: Convert the volume of acetone liquid to grams
To calculate the mass of acetone required, we need to convert the volume from liters to grams. The specific gravity is given as 0.781, which means that 1 liter of acetone weighs 0.781 times the weight of 1 liter of water.
Since the molecular weight of acetone is given as 58 g/mol, the weight of 1 liter of acetone is equal to 58 grams. Therefore:
Weight of acetone (in grams) = Volume of acetone (in liters) x Specific gravity
= 120000 liters x 0.781
= 93720 grams
Step 4: Convert the mass of acetone to moles
To convert the mass of acetone to moles, we need to divide the weight by the molecular weight:
Moles of acetone = Weight of acetone (in grams) / Molecular weight
= 93720 grams / 58 g/mol
= 1614.483 moles
Step 5: Calculate the moles of acetone required to achieve the desired concentration
The desired concentration is given as 200 ppm by volume, which means 200 parts of acetone per million parts of air. To convert this to a mole fraction, we need to divide the desired concentration by the total volume of air:
Mole fraction of acetone = (Desired concentration / 1,000,000) / (1 - Desired concentration / 1,000,000)
Plugging in the values, we get:
Mole fraction of acetone = (200 / 1,000,000) / (1 - 200 / 1,000,000)
= 0.0002 / 0.9998
= 0.000200040008002
Step 6: Calculate the moles of acetone required
The mole fraction of acetone is the ratio of moles of acetone to the total moles of air. In this case, the total moles of air is essentially the same as the moles of acetone:
Moles of acetone = Mole fraction of acetone
Therefore, the moles of acetone required is approximately 0.000200040008002.
Step 7: Convert moles of acetone to volume in liters
Finally, we can calculate the volume of acetone liquid required by converting the moles of acetone to liters. Since the density of acetone is not given, we will assume an ideal gas and use the ideal gas law at standard temperature and pressure (STP) to calculate the volume:
Volume of acetone (in liters) = Moles of acetone x (22.414 liters/mol)
= 0.000200040008002 x 22.414
= 0.004484647169 worth rounding to 0.0045 liters
Therefore, approximately 0.0045 liters (or 4.5 milliliters) of acetone liquid are required to produce a vapor concentration of 200 ppm by volume in the given room.
To determine the volume of acetone needed, we need to use the formula for calculating ppm concentration in a gas mixture:
ppm = (V/Vt) * 10^6
Where:
- ppm is the desired concentration in parts per million (200 ppm in this case)
- V is the volume of the solute (acetone) in liters
- Vt is the total volume of the mixture in liters
In this case, we want to find V, the volume of acetone.
First, let's convert the dimensions of the room to liters:
- Length = 3 meters = 300 cm = 3 liters
- Width = 4 meters = 400 cm = 4 liters
- Height = 10 meters = 1000 cm = 10 liters
The total volume of the room (Vt) is the product of these dimensions:
Vt = Length * Width * Height = 3 liters * 4 liters * 10 liters = 120 liters
Now we can substitute the values into the ppm formula and solve for V:
200 ppm = (V/120) * 10^6
To isolate V, we multiply both sides by Vt and divide by 10^6:
V = (200 ppm * Vt) / 10^6
V = (200 * 120) / 10^6
V = 24 / 10^6
V ≈ 0.000024 liters
Since the specific gravity of acetone is given as 0.781, we can find the mass of the acetone needed using the specific gravity formula:
Specific Gravity = density of substance / density of reference substance
Assuming water as the reference substance (density of water = 1 g/cm^3), the density of acetone can be calculated as follows:
density of acetone = (Specific Gravity) * (density of water)
density of acetone = (0.781) * (1 g/cm^3)
density of acetone = 0.781 g/cm^3
Now, we can find the mass of acetone using the volume calculated earlier:
Mass = density * volume
Mass = (0.781 g/cm^3) * (0.000024 liters) = 0.000019 g
Finally, we can use the molecular weight of acetone to convert the mass into milliliters:
Milliliters = mass / molecular weight
Milliliters = 0.000019 g / 58 g/mol ≈ 0.000000328 mol
Since we have the density of acetone and we are given that the temperature is 25°C and the pressure is 1 atm, we can use the ideal gas law to calculate the volume:
PV = nRT
Where:
- P is the pressure in atm (1 atm)
- V is the volume in liters (unknown)
- n is the number of moles (0.000000328 mol)
- R is the ideal gas constant (0.0821 L*atm/(mol*K))
- T is the temperature in Kelvin (25°C + 273 = 298 K)
Rearranging the formula to solve for V:
V = (nRT) / P
V = (0.000000328 mol * 0.0821 L*atm/(mol*K) * 298 K) / 1 atm
V ≈ 0.000008 liters = 0.008 ml
Therefore, approximately 0.008 milliliters of acetone liquid is required to produce a vapor concentration of 200 ppm in the given room.