Respuesta :
Answer:
1460 red Lego bricks will be sufficient for 10 kg child to consume to reach the LD-50 threshold.
Explanation:
Average mass of a Lego brick = 2.50 grams
Amount of cadmium in 1 gram of red lego brick = 274 μg = [tex]0.000274 g[/tex]
1 μg = [tex]10^{-6} g[/tex]
Amount of cadmium in 2.50 grams of lego brick :
[tex]2.50 g\times 0.000274 g=0.000685 g[/tex]
LD-50 for cadmium = 100 mg/kg
For a 10.0 kg child the amount of cadmium that will be lethal :
[tex]100mg/kg\times 10.0 kg=1000 mg = 1 g[/tex]
1 g = 1000 mg
Let the number of red Lego bricks ingested by the child to reach the LD-50 threshold be x.
x × (Amount of Cd in single 2.50 g red lego brick) = 1g
[tex]x\times 0.000685 g=1 g[/tex]
[tex]x=\frac{1 g}{0.000685 g}=1459.85\approx 1460 [/tex]
1460 red Lego bricks will be sufficient for 10 kg child to consume to reach the LD-50 threshold.
A 10.0 kg child would have to consume 1.46 × 10³ Lego bricks, with an average mass of 2.50 g, to reach the LD50 threshold for cadmium of 100 mg/kg.
The lethal dose 50 (LD50) for cadmium is 100 mg Cd/kg body mass. The mass of Cd a 10.0 kg child would need to consume to reach the LD50 threshold is:
[tex]10.0 kg body\ mass \times \frac{100 mgCd}{1kg\ body\ mass} \times \frac{1gCd}{1000mgCd} = 1.00 g Cd[/tex]
There are 274 μg (274 × 10⁻⁶ g) of Cd per gram of Lego brick. The mass of Lego brick that contains 1.00 g of Cd is:
[tex]1.00 g Cd \times \frac{1gBrick}{274 \times 10^{-6}gCd } = 3.65 \times 10^{3} gBrick[/tex]
The average mass of a Lego brick is 2.50 g. The number of bricks that have a mass of 3.65 × 10³ g are:
[tex]3.65 \times 10^{3} gBrick \times \frac{1Brick}{2.50 gBrick} = 1.46 \times 10^{3} Brick[/tex]
A 10.0 kg child would have to consume 1.46 × 10³ Lego bricks, with an average mass of 2.50 g, to reach the LD50 threshold for cadmium of 100 mg/kg.
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