intro chemistry

Question

You are on the management team of a company that is considering purchasing a tanker truck. The truck you want has a volume of 26,000 liters and an empty mass/weight of 15,500 kg. However, the route you wish to travel has a bridge with a weight limit of 25 tons. If you purchase the truck and fill it to capacity with a liquid whose density is 0.85 kg/L,what will the mass of the truck be?

and what is the max volume you will be able to legally transport

Answer 1

First I state what is given and what I want , include all the units in these statement. It is easy to get lost with out them. The units and their conversions can lead you in the right direction.

Part 1 -find the mass of the liquid in the truck

GIVEN

Volume of truck: 26,000 liters

Weight of empty truck: 15,500 kg ( we will use this in part 2)

(I am not going to enter weight limit here , that will be part of part 2)

Density of liquid; .85kg/L

WANTED

Mass of liquid in the truck in kg ( in part 2 we will add it to the mass of the truck and covert total to tons)

Set up equation, solve for mass of volume in the truck

26,000 liters X .85kg/l = 22,100. kg mass of the liquid in the truck

Part 2 lets add the mass of the liquid to the mass of the truck then convert the answer to tons

( on a test you mat be given certain conversion factors, and some you may have to memorize )

Given

1kg= 2.2 lb this is a conversion factor, it can be written as 1kg/2.2 lb or 2.2 lb/1kg

1 ton=2,000 lb also a conversion factor, it can be written as 1ton/2000lb or 2000lb/1ton

Mass of liquid in truck : 22,100 kg

Mass of truck: 15,500kg

Wanted

mass of truck and liquid in tons

22,100 kg +15,500kg =37,600 kg this is the total mass, now lets convert to tons

( on a test you mat be given certain conversion factors, and some factors you may have to memorize )

37,6000 kg x 2.2 lb/kg x 1 ton/2000lb = 41.4 tons

When I have a conversion problem, like this I like to start with the amount that is not a fraction, in other not a lb/kg or a ton/ lb . If I start with kg as above my first conversion factor needs to be kg on the bottom of the fraction. In that way it cancels out, the kg and my answer would be in pounds. But I dont want pounds , so my next conversion factor must have pounds on the bottom of the fraction , pounds cancel out and I an left with my answer in tons.

Now lets compare it to the 25 ton weight limit

Answer 2

This is a problem dealing with CONVERSIONS. We will use dimensional analysis to help solve the problem.

Ultimately, we need to find the total mass/weight of the truck + contents in tons, and compare this value to the limit of 25 tons.

Mass of contents (in tons):

26,000 liters x 0.85 kg / liter = 22,100 kg

22,100 kg x 2.20 lbs / kg = 48,620 lbs

48,620 lbs x 1 ton / 2000 lbs = 24.31 tons

Mass of truck (in tons):

15,500 kg x 2.20 lbs / kg x 1 ton / 2000 lbs = 17.05 tons

Total mass of truck + contents = 24.3 + 17.1 = 41.4 tons (exceeds the weight limit of 25 tons)

To find the maximum volume of material that can be transported, we will deduct the mass of the truck (17.05 tons) from the weight limit (25 tons) and then convert that value to liters, using the known density of the liquid.

Maximum mass of liquid allowed:

25 tons - 17.1 tons = 7.9 tons of liquid allowed

Maximum volume of liquid allowed:

7.9 tons x 2000 lbs / ton = 15,800 lbs

15,800 lbs x 1 kg / 2.2 lbs = 7,182 kg

7,182 kg x 1 L / 0.85 kg = 8449 Liters of liquid allowed