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 ft 12.5 ft 7.3 ft?
i made ft^3 into Liters and got 8,346,211.799 then I made the grams into kilograms and set up density = mass/volume and solved for x(mass) I got the answer to be 9.93e3. but that is wrong. what am i doing wrong? please help! thanks :)
nevermind! i converted wrong!
To find the mass of the air in the room, you correctly converted the volume from cubic feet (ft^3) to liters (L) by multiplying it by 28.3168. So, the volume of the room is 12.0 ft * 12.5 ft * 7.3 ft * 28.3168 = 29,605.4472 L.
Next, you set up the equation density = mass/volume and solved for mass. The density is given as 1.19 g/L. Since the volume is now in liters, you can use the given density directly.
Let's set up the equation:
1.19 g/L = mass (in grams) / 29,605.4472 L
To solve for mass, multiply both sides of the equation by the volume:
mass (in grams) = 1.19 g/L * 29,605.4472 L
mass (in grams) = 35,234.5259 g
Now, to convert the mass from grams to kilograms, divide by 1000:
mass (in kilograms) = 35,234.5259 g / 1000
mass (in kilograms) = 35.2345 kg (rounded to four decimal places)
So, the mass of the air in the room is approximately 35.2345 kilograms.