It is estimated that uranium is relatively common in the earth’s crust, occurring in amounts of 4 g/metric ton. A metric ton is 1000 kg. At this concentration, what mass of uranium is present in 1.0 mg of the earth’s crust?
Use ratio/proportion as follows:
(4 g/1 x 10^6 g) = (x g/1 x 10^-3 g)
solve for x.
Or set it up by dimensional analysis.
1 x 10^-3(crust) x (4 g U/1 x 10^6 g C) = ??
Check my arithmetic. It looks like 4 x 10^-9 g or 4 ng/metric ton.
Well, let me do some math, but prepare yourself for some fun! So, first, we need to convert the 1.0 mg to grams. Since there are 1000 milligrams in a gram, we divide 1.0 mg by 1000, which gives us 0.001 grams.
Now that we have 0.001 grams, we can compare it to the concentration of uranium in the earth's crust, which is 4 grams/metric ton.
To find out how much uranium is present in 1.0 mg of the crust, we need to set up a proportion.
0.001 g / X = 4 g / 1000000 g
Cross multiplying, we get X = (0.001 g) * (1000000 g) / 4 g, which simplifies to 250 grams.
So, according to my calculations, there is a whopping 250 grams of uranium in just 1.0 mg of the earth's crust. That's a lot for such a tiny amount! It's like finding gold in a sand grain.
To find the mass of uranium in 1.0 mg of the earth's crust, we need to convert the concentration from g/metric ton to mg/kg, and then multiply it by the given mass.
Given:
Concentration of uranium = 4 g/metric ton
1 metric ton = 1000 kg
1 kg = 1000 g
To convert concentration from g/metric ton to mg/kg, we can use the following conversion factors:
1 g = 1000 mg
1 metric ton = 1000 kg
Concentration in mg/kg = (4 g/metric ton) * (1000 mg/g) * (1 metric ton/1000 kg)
Concentration in mg/kg = 4000 mg/kg
Now we can calculate the mass of uranium in 1.0 mg of the earth's crust:
Mass of uranium = Concentration in mg/kg * Mass of the earth's crust
Mass of uranium = 4000 mg/kg * 1.0 mg
Mass of uranium = 4000 mg²/kg
Therefore, the mass of uranium in 1.0 mg of the earth's crust is 4000 mg²/kg.
To find the mass of uranium in 1.0 mg of the Earth's crust, we need to use the concentration given in the question.
Given:
- Concentration of uranium: 4 g/metric ton
- Metric ton: 1000 kg = 1,000,000 g (since 1 kg = 1000 g)
To calculate the mass of uranium in 1.0 mg, we can follow these steps:
Step 1: Convert the concentration to grams per milligram (mg):
Since there are 1,000,000 g in a metric ton, we divide the concentration by 1,000,000 to convert it to grams per mg.
Concentration = 4 g/metric ton = (4 g/metric ton) / (1,000,000 mg/g) = 4 x 10^-6 g/mg
Step 2: Multiply the concentration by the mass in mg:
Mass of uranium in 1.0 mg = (4 x 10^-6 g/mg) * 1.0 mg = 4 x 10^-6 g
Therefore, there is approximately 4 x 10^-6 grams (or 0.000004 grams) of uranium present in 1.0 mg of the Earth's crust.