The density of air at ordinary atmospheric pressure and 25°C is 1.19 g/L. What is the mass, in kilograms, of the air in a room that measures 12.0 multiplied by 15.5 multiplied by 8.4 ft?
Convert 12.0, 15.5, and 8.4 feet to cm.
Convert measurements to volume; i.e. length(cm) x width(cm) x height(cm) = volume in cc.
Change volume in cc to volume in L.
Then d = m*v. You have v and d, solve for m in grams and convert to kg.
Post your work if you get stuck.
To calculate the mass of air in the room, we need to convert the room's volume from cubic feet to liters. Then, using the density of air, we can find the mass.
1. Convert the dimensions of the room from feet to centimeters:
- Length: 12.0 ft = 12.0 ft × 30.48 cm/ft = 365.76 cm
- Width: 15.5 ft = 15.5 ft × 30.48 cm/ft = 472.02 cm
- Height: 8.4 ft = 8.4 ft × 30.48 cm/ft = 256.03 cm
2. Calculate the volume of the room in cubic centimeters:
- Volume = Length × Width × Height
- Volume = 365.76 cm × 472.02 cm × 256.03 cm = 43,901,337.73 cm³
3. Convert the volume from cubic centimeters to liters:
- 1 cm³ = 1 mL = 0.001 L
- Volume = 43,901,337.73 cm³ × 0.001 L/cm³ = 43901.34 L
4. Use the density of air to find the mass of the air in the room:
- Density of air = 1.19 g/L
- Mass = Density × Volume
- Mass = 1.19 g/L × 43901.34 L = 52,308.82 g
5. Convert the mass from grams to kilograms:
- 1 kg = 1000 g
- Mass = 52,308.82 g × (1 kg / 1000 g) = 52.31 kg
Therefore, the mass of the air in the given room is approximately 52.31 kilograms.