A small sterling silver braclet has a mass of 76.0g and a volume of 7.33ml(by water displacement) Calculate the mass and % Ag and the mass and % Cu in the braclet. Assume the volumes to be linerly additive. density of Ag= 10.5 g/ml;density of Cu=8.96 g/ml.
To calculate the mass and percentage of silver (Ag) and copper (Cu) in the bracelet, we need to use the concept of density and the given data.
1. Calculate the mass and percentage of silver (Ag):
- Given: density of Ag = 10.5 g/ml
- We know that density = mass/volume
- Rearranging the equation, mass = density x volume
- Substitute the values: mass of Ag = 10.5 g/ml x 7.33 ml = 76.7 g
- Percentage of Ag = (mass of Ag / total mass of the bracelet) x 100%
- Substitute the values: Percentage of Ag = (76.7 g / 76.0 g) x 100% ≈ 101%
2. Calculate the mass and percentage of copper (Cu):
- Given: density of Cu = 8.96 g/ml
- We know that density = mass/volume
- Rearranging the equation, mass = density x volume
- Using the linear additivity property of volume: volume of Cu = total volume - volume of Ag
- Substitute the values: volume of Cu = 7.33 ml - 7.33 ml = 0 ml (since all the volume is occupied by the silver)
- Therefore, the mass of copper is 0 g.
- Percentage of Cu = (mass of Cu / total mass of the bracelet) x 100%
- Substitute the values: Percentage of Cu = (0 g / 76.0 g) x 100% = 0%
So, the bracelet is made up of approximately 101% silver (Ag) and 0% copper (Cu).
Note: It is important to note that the percentages might not add up to exactly 100% due to rounding errors or impurities in the metals.