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A nugget of gold with a mass of 521 g is added to 50.0 mL of water. The water level rises to a volume of 77.0 mL. What is the density of the gold?
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A nugget of gold with a mass of 521 g is added to 50.0 mL of water The water level rises to a volume of 77.0 mL What is the density of the gold?
Assuming the gold nugget is solid and pure (unlikely in real life!) The volume of the nugget is 77.0 - 50.0 mL = 27.0 mL So density = mass/volume = 521/27.0 = 19.3 g per mL.
What is the difference between volume and density?
Simply: Volume (V) is how much space an object takes up whereas density is how "compressed" an objects mass (m) is. Density = m/V Example: Imagine a ton of feathers and a ton of iron. They both have the same mass (weight) but they have different volumes and density.
A piece of metal with a mass of 167 g is placed in a 50 mL graduated cylinder The water level rises from 20 mL to 36 mL What is the density of the metal?
Density = mass/volume = 167g/ (volume displaced) = 167g / (36mL - 20mL) = 167g/16mL = 10.4g/mL. Density is usually recorded in g/cm3 which is the same as g/mL so the density is 10.4g/cc. Also, to be extra correct, the answer should be rounded to 10g/cc because 16mL only has 2 significant figures so that is the number you report in your final answer.
A piece of metal with a mass of 163 g is placed in a 50 mL graduated cylinder The water level rises from 20 mL to 36 mL What is the density of the metal?
The volume of the piece of metal is measured by the difference in the volume of water in the graduated cylinder before and after the piece of metal is placed in the cylinder. This is stated to be 36 - 20 = 16 mL. Density is defined to be mass per unit volume. Therefore, for this piece of metal the density is 163/16 = 10 g/mL. (Only two significant digits are justified, because the is the number of significant digits in the limiting datum 16.)
Can you calculate the volume of an item without knowing the density?
It is quite simple if it is a regular shaped object like a cylinder or a cube. For example if you wanted calculate the volume of a cylinder you need to know the radius of the circular cross-section of the cylinder - this is the measurement from the centre of the circle, to the outer-edge and then multiply that by the height of the cylinder. For irregular shaped objects don't think there is a simple mathematical way if you don't know the density but you can always use water displacement to get a volume measurement. Just drop the object you want to know the volume off into a graduated cylinder partially filled with water - the amount the level rises will be roughly equal to the volume of the object you dropped in.
