Respuesta :
Answer:
(a) Mass of gold = 0.0073223 kg.
(b) V of gold 3.79 x 10⁻⁷ m³ & ∴ V of copper = 7.438 x 10⁻⁸ m³.
(c) The density of the British sovereign coin 17,620 kg/m³.
Explanation:
(a) Find the mass of gold in the sovereign in kilograms using the fact that the number of karats = 24 (mass of gold)/(total mass).
∵ the number of karats = 24 (mass of gold)/(total mass)
the number of karats = 22-karat gold,
mass of gold = ??? g,
total mass = 7.988 g.
∴ mass of gold = (the number of karats)(total mass)/24 = (22)(7.988 g)/(24) = 7.3223 g = 0.0073223 kg.
(b) Calculate the volumes of gold and copper, respectively.
∵ Mass of coin = 7.988 g.
∵ mass of gold = 7.3223 g.
∴ mass of Cu = Mass of coin - mass of gold = 7.988 g - 7.3223 g = 0.6657 g = 0.6657 x 10⁻³ kg.
- To find the volume of Copper and gold, we can use the relation:
V = m/d.
where, V is the volume of the material,
m is the mass of the material,
d is the density of the material.
- For gold:
Density of gold = 19,320 kg/m³, mass of gold = 0.0073223 kg.
∴ V of gold = m/d = (0.0073223 kg)/(19,320 kg/m³) = 3.79 x 10⁻⁷ m³.
- For copper:
Density of copper = 8,950 kg/m³, mass of copper = 0.6657 x 10⁻³ kg.
∴ V of copper = m/d = (0.6657 x 10⁻³ kg)/(8,950 kg/m³) = 7.438 x 10⁻⁸ m³.
(c) Calculate the density of the British sovereign coin. kg/m³.
- To find the density of the British sovereign coin, we can use the relation:
d = m/V.
mass of the British sovereign coin = 7.988 g = 0.007988 kg.
Volume of the British sovereign coin = V of gold + V of copper = (3.79 x 10⁻⁷ m³) + (7.438 x 10⁻⁸ m³) = 4.534 x 10⁻⁷ m³.
∴ Density of the British sovereign coin = m/V = (0.007988 kg)/(4.534 x 10⁻⁷ m³) = 17,620 kg/m³.
Based on the relationships between mass, volume and density;
- mass of gold in the sovereign is 0.0073223 kg
- the volume of gold is 3.79 x 10⁻⁷ m³ while the volume of copper is 7.438 x 10⁻⁸ m³
- the density of the British sovereign coin 17,620 kg/m³.
What is the the relationships between mass, volume and density?
The mass, volume and density of a substance are related by the formula given below:
- Density = mass/volume
a) Using the fact that the number of karats = 24 (mass of gold)/(total mass). kg;
the number of karats = 24 (mass of gold)/(total mass)
the number of karats = 22-karat gold,
total mass = 7.988 g.
- mass of gold = (the number of karats)(total mass)/24
mass of gold = (22)(7.988 g)/(24) = 7.3223 g
mass of gold = 0.0073223 kg.
(b) The volume of gold and copper are calculated thus:
- Mass of coin = 7.988 g.
- mass of gold = 7.3223 g.
mass of copper = Mass of coin - mass of gold
mass of copper = 7.988 g - 7.3223 g = 0.6657 g
mass of copper = 0.6657 x 10⁻³ kg.
From the formula above:
- Volume = mass /density
Thus;
Density of gold = 19,320 kg/m³, mass of gold = 0.0073223 kg.
Volume of gold = 0.0073223 kg/19,320 kg/m³
Volume of gold = 3.79 x 10⁻⁷ m³
Also,
Density of copper = 8,950 kg/m³, mass of copper = 0.6657 x 10⁻³ kg.
volume of copper = (0.6657 x 10⁻³ kg)/(8,950 kg/m³)
Volume of copper = 7.438 x 10⁻⁸ m³.
(c) the density of the British sovereign coin is then calculated using the formula:
- density = mass/volume
mass of the British sovereign coin = 7.988 g = 0.007988 kg.
Volume of the British sovereign coin = volume of gold + volume of copper = (3.79 x 10⁻⁷ m³) + (7.438 x 10⁻⁸ m³) = 4.534 x 10⁻⁷ m³.
Then;
Density of the British sovereign coin = (0.007988 kg)/(4.534 x 10⁻⁷ m³)
Density of the British sovereign coin = 17,620 kg/m³.
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