What is likely identity of a metal, if a sample has a mass of 67.5g when measured in air and an apparent mass of 59.5g when submerged in water?
To determine the likely identity of the metal, we can use Archimedes' principle, which states that the buoyant force on an object submerged in a fluid is equal to the weight of the fluid displaced.
First, we need to calculate the buoyant force acting on the metal when it is submerged in water. The weight of the water displaced is equal to the difference in the mass of the metal when measured in air and when submerged in water.
Weight of water displaced = mass in air - mass in water = 67.5g - 59.5g = 8g
Now, since the buoyant force is equal to the weight of the displaced water, we can calculate the volume of water displaced by dividing the weight of water displaced by the density of water.
Density of water = 1g/cm³
Volume of water displaced = weight of water displaced / density of water = 8g / 1g/cm³ = 8cm³
Finally, we can compare the volume of water displaced to the volume of the metal to determine its likely identity. If the volume of water displaced is equal to the volume of the metal, then the metal is likely pure, with no impurities. If the volume of water displaced is less than the volume of the metal, then it is likely a mixture or alloy.
However, without information about the actual volume of the metal, it is not possible to determine its likely identity based solely on the provided data.
To determine the likely identity of a metal based on its mass measurements in air and water, we need to understand the concept of buoyancy and the principle of Archimedes.
When a solid object is submerged in a fluid, it experiences an upward force called buoyant force. According to Archimedes' principle, this buoyant force is equal to the weight of the fluid displaced by the object.
Here's how we can calculate the volume of the metal and determine its identity:
1. Calculate the weight of the displaced water:
Since the mass of the metal measured in air is 67.5g, its weight (considering gravity) is also 67.5g.
2. Calculate the apparent weight of the metal in water:
The apparent weight of the metal is the difference between its weight in air and its weight when submerged in water. In this case, the apparent weight is 67.5g - 59.5g = 8g.
3. Calculate the weight of the displaced water:
The apparent weight of the metal is equal to the weight of the displaced water. Therefore, the weight of the displaced water is also 8g.
4. Calculate the volume of the displaced water:
The density of water is approximately 1g/cm³. Therefore, the volume of the displaced water is 8 cm³ since density = mass/volume.
5. Calculate the volume of the metal:
As established in step 4, the volume of the displaced water is equal to the volume of the metal. Therefore, the volume of the metal is also 8 cm³.
Now, to determine the identity of the metal, we need to compare its volume (8 cm³) with the known densities of different metals. Consult a reference table or database to check which metal has a density close to 8 cm³/g. The metal with the closest density match is likely the one you're looking for.
Keep in mind that this method provides an estimation based on the assumption that the metal is a pure substance. If the metal is an alloy or contains impurities, the density may differ. Additionally, variations in temperature and atmospheric pressure may affect the results.
By Archimedes principle, the weight of a submerged object is reduced by the weight of liquid it displaces.
Weight of metal in air = 67.5 g
Weight in water = 59.5
weight of water displaced =67.5-59.5=8 g
density of water = 1.0 g / ml
volume of water displaced = 8 / 1.0 ml = 8 ml
volume of metal = 8 ml
density of metal = 67.5/8 = 8.44 g/ml
From a list of density of elements, we find, in ascending order:
7.87 Iron, Fe
7.9 Gadolinium, Gd
8.23 Terbium, Tb
8.55 Dysprosium, Dy
8.57 Niobium, Nb
8.65 Cadmium, Cd
8.8 Holmium, Ho
8.9 Nickel, Ni
8.9 Cobalt, Co
Make your choice from the list depending on the likelihood of weighing exotic metals. To me, likely choices are among Iron, Cadmium, Nickel and Cobalt.
Ref: http://www.lenntech.com/periodic-chart-elements/density.htm#ixzz0pVbYQMDV