Question

You just ordered a batch of sodium hydroxide (NaOH) which is used to lower the pH of a solution during a process your team supervises. You need to get a quote for transportation from the closest port to your company's facility, but the trucking company charges by the ton and you don't know how much your load weighs. The international vendor is closed and you can't call to ask due to the time zone difference so you just have to figure it out.

According to the manufacturer, the density of NaOH is 52.3 Ib/ft^3. It shipped in cylindrical drums which are 22.5 inches in diameter and 33.5 inch tall and weigh 27.4 Ibs when empty. The shipping container is 8.0ft wide, 8.5 ft tall, and 20.0ft long. The empty shipping container weighs 5,000 Ibs.

(a) Assuming the drums are filled to capacity, calculate the mass of a single drum of NaOH. [mass = volume x volume]

(b) Calculate the total number of drums which can fit into the shipping container assuming they are packed in even rows and stacked on top if possible. [Hint: You can't have a fraction of a drum, it would leak all over. They get stacked just like boxes]

(c) Calculate the total mass of the shipping container full of drums and be ready to get a quote from the trucking company tomorrow.

(d) How does the total mass of the shipping container change if the diameter and height of the drums decreases by exactly 50%. Assume that the mass of the empty drums scales linearly with volume. In other words, if the volume decreases by 1/3, then the mass will also decrease by 1/3.

Answer 1

The solution to this problem involves simple unit conversions and most importantly the best arrangement of drums in container.

The solution with complete procedure is given below.