A 2.60 kg steel gas can holds 15.0 L of gasoline when full. What is the average density of the full gas can, taking into account the volume occupied by steel as well as by gasoline?
Please show the steps, thanks.
Please see answer to ques by Charlie July18 8:28pm
To find the average density of the full gas can, we need to calculate the total mass and the total volume occupied by both the steel can and the gasoline. Once we have these values, we can divide the total mass by the total volume to find the average density.
Step 1: Calculate the mass of the steel can
The mass of the steel can is given as 2.60 kg.
Step 2: Calculate the mass of the gasoline
To find the mass of the gasoline, we need to know its density. The density of gasoline varies depending on factors like temperature and additives. However, for this problem, let's assume a standard density of 0.75 kg/L. Since the gasoline fills 15.0 L, we can calculate the mass of the gasoline by multiplying the density by the volume.
Mass of gasoline = (Density of gasoline) x (Volume of gasoline)
Mass of gasoline = 0.75 kg/L x 15.0 L = 11.25 kg
Step 3: Calculate the total mass
The total mass is the sum of the mass of the steel can and the mass of the gasoline.
Total mass = Mass of steel can + Mass of gasoline
Total mass = 2.60 kg + 11.25 kg = 13.85 kg
Step 4: Calculate the total volume
The total volume is the sum of the volume occupied by the steel can and the volume occupied by the gasoline.
Total volume = Volume of steel can + Volume of gasoline
Total volume = 15.0 L + 15.0 L = 30.0 L
Step 5: Calculate the average density
Average density = Total mass / Total volume
Average density = 13.85 kg / 30.0 L
Now, divide the mass by the volume and get the value of average density.
Using a unit conversion, 1 L = 1 dm^3.
Average density = 13.85 kg / (30.0 dm^3)
Average density = 0.4617 kg/dm^3
So, the average density of the full gas can, taking into account the volume occupied by steel as well as by gasoline, is 0.4617 kg/dm^3.