To find the amount of moles, we need to first find the weight of each part of the compound we are looking at. Sodium (Na) weighs about .  Oxygen (O) weighs about .  Hydrogen weighs about .  One mole of NaOH would weigh .

Now we can convert grams to moles using basic stoichiometry.

We know the following relationships from the information in the problem and from the definitions of the units:

Solving the problem:

The change in volume after you submerge your metal in the container is the volume of the metal itself. Therefore:

Since the densities we have been given are all expressed as  we should convert our numbers into those units as shown below:

Now that we have both the mass and volume of our unknown metal you can calculate the density of the metal because density is defined as:

So the density of our metal is 

Since our metal's density matches the density of copper we can now prove that the metal is pure copper.

Remember, there are 2.54 centimeters in every one inch. 2.54 can be multiplied by the given number of inches in order to cancel units, and convert the inches to centimeters. Answer with the same number of significant figures, as what was given in the initial number.

Remember: there are approximately 1.06 quarts for every 1 liter; so if the given number of liters is multiplied by 1.06, it will convert the units to quarts. Make sure the answer and the given amount have the same number of significant figures.

Remember, the prefix "kilo" means "thousand." So there are a thousand grams, for every 1 kilogram. There are approximately 454 grams per pound, so arrange those conversion in such a way that units cancel, and pounds are the only units left. Make sure the answer and the given amount have the same number of significant figures (22 kg).

This is a multi-step conversion. A U.S. to metric conversion will be needed at some point because the initial measurement is in yards (a U.S. measurement) and the answer requires meters (a metric unit). To use the  conversion; change yards into inches. Once in centimeters, remember that there are 100cm in 1m; "centi" means "hundred."

The questions gives a U.S. measurement (tons) and asks for a metric unit (grams), so at some point, a U.S. measurement to metric measurement conversion will be used. There are approximately 454 grams (metric unit) per 1 pound (U.S. measurement); so tons needs to be changed into pounds in order to use that conversion. Make sure the units cancel and make sure the answer has the same number of significant figures as the given measurement.

Remember: 

In this problem we are given the density and the volume and asked to calculate the mass. Thus, by solving the above equation for mass, we get: 

Therefore, we can simply plug in our values for  and : 

However, we need to check out significant figures. 10.5 has three significant figures, and 950 has two significant figures. Therefore our answer can only have two significant figures. Therefore our answer is 9500g, written in scientific notation: 

Remember: 

Therefore to find density we must divide the given mass by the given volume.

However, we must remember our significant figure rules. In this case both the given values have 4 significant figures. So, our answer can only have 4 significant figures. Therefore after rounding the correct answer is .