One troy ounce of gold is worth $380. There are 33.8 grams per troy ounce. You have a stock colloidal solution of a very fine gold dust. Its concentration is .1% w/v. from this solution, 1 ml is placed in 9 ml of an isotonic, pH buffered solution to make a working stock. An assay calls for .5 ml of this working stock to which is added .1 ml of serum. What is the cost of hold used for each test?
My work is this and I am not sure if it is correct:
.1g/100= .001g gold
.001 g gold/ml * .5 ml = .00005 g gold
.00005/.6ml = 8.33 *10^-5
8.33 *10^-5 * 100= 8.33 *10^-3 % w/v
.00005*1 troy ounce/33.8 g = 1.48*10^-6
1.48*10^-6 *$380 = $5.6*10^-4
Any help would be greatly appreciated. Thanks!
I agree with some of what you have but not all of it. Here is your work.
.1g/100= .001g gold
I agree with 1E-3g Au
.001 g gold/ml * .5 ml = .00005 g gold
0.001 x 0.5 = 5E-4--you have 5E-5.
The rest of this I don't get. It appears to me that all of the Au you have at this point, and all the Au being used in the assay, is 5E-4g so the price to this point is 5E-4g x 380/33.8g = 5.62E-3 and I guess that is dollars.
I don't know where the 0.6 mL comes from and I don't follow the rest of your work; however, having said that I note that your answer is just a factor of 10 from my answer and that is a direct result of that first mistake above of 5E-5 for 5E-4. So I would think you did a good job but did a lot of extra work that wasn't needed.
.00005/.6ml = 8.33 *10^-5
8.33 *10^-5 * 100= 8.33 *10^-3 % w/v
.00005*1 troy ounce/33.8 g = 1.48*10^-6
1.48*10^-6 *$380 = $5.6*10^-4
To calculate the cost of gold used for each test, we need to determine the amount of gold that is present in the final solution.
Let's break down the calculations step by step:
1. Concentration of gold in the colloidal solution:
- Given: Concentration = 0.1% w/v
- This means there are 0.1 grams of gold in 100 milliliters of solution.
- Convert 0.1% w/v to grams per milliliter: 0.1g/100ml = 0.001g/ml
2. Volume of gold solution used to make the working stock:
- 1 milliliter (ml) of the colloidal solution is added to 9 milliliters of isotonic, pH buffered solution.
- Therefore, the total volume of the working stock is 10 milliliters (1ml + 9ml).
3. Amount of gold in the working stock:
- Multiply the volume of the working stock by the concentration of gold in the colloidal solution:
10ml * 0.001g/ml = 0.01 grams of gold in the working stock.
4. Amount of gold used in each test:
- The assay requires 0.5 milliliters (ml) of the working stock to be used.
- Calculate the amount of gold in 0.5 ml of the working stock:
0.5ml * 0.001g/ml = 0.0005 grams of gold.
5. Calculate the cost of gold used in each test:
- Convert the amount of gold used in grams to troy ounces:
0.0005 grams * (1 troy ounce / 31.1035 grams) = 1.607 × 10^-5 troy ounces of gold.
- Calculate the cost of gold, given that 1 troy ounce is worth $380:
cost = 1.607 × 10^-5 troy ounces * $380 = $0.0060896
Therefore, the cost of gold used for each test is approximately $0.0061.