Final answer:
To calculate the concentration of m-xylene spilled in a laboratory, you need to convert the volume of the room to cubic meters, then calculate the mass of m-xylene in milligrams, and then divide the mass by the volume to get the concentration in mg/m³. To find ppmv, determine the number of moles of m-xylene at NTP and its volume, followed by finding the ratio of this volume to the lab volume expressed in parts per million.
Step-by-step explanation:
The question requires us to calculate the concentration of m-xylene (C8H10) in mg/m3 after it has completely evaporated into a laboratory space with the dimensions of 20 ft x 40 ft x 9 ft. To start, we'll convert the lab volume to cubic meters (1 ft = 0.3048 m):
- Volume = length × width × height = (20 ft × 0.3048 m/ft) × (40 ft × 0.3048 m/ft) × (9 ft × 0.3048 m/ft)
- Volume = 6.096 m × 12.192 m × 2.7432 m = 203.8611456 m3
- The mass of 625 ml of m-xylene, assuming a density of approximately 0.86 g/ml (typical for xylene), would be: Mass = 625 ml × 0.86 g/ml = 537.5 g
- Now convert the mass to mg: 537.5 g × 1000 mg/g = 537500 mg
Then, to find the concentration in mg/m3 we divide the mass by the volume:
- Concentration = 537500 mg / 203.8611456 m3
- Concentration = 2636.94 mg/m3
To estimate the concentration in ppmv (parts per million by volume), we must use the ideal gas law at NTP (Normal Temperature and Pressure). The molar mass of m-xylene is 106.17 g/mol and at NTP, one mole of any ideal gas occupies 22.414 liters (0.022414 m3).
- We first find the number of moles of m-xylene: n = 537.5 g / 106.17 g/mol
- n = 5.062 moles of m-xylene
- Next, find the volume that these moles would occupy at NTP: V = n × 22.414 L/mol
- V = 5.062 moles × 22.414 L/mol = 113.50908 L = 0.11350908 m3
- To calculate ppmv, we find the ratio of the volume of m-xylene to the total volume × 106:
- ppmv = (0.11350908 m3 / 203.8611456 m3) × 106
- ppmv = 556.46 ppmv