I think I have this problem figured out correctly, but is there anyone who can tell me if I'm doing something wrong.
The question is...
"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. It's concentration is .10% w/v. From this solution 1.0 ml is placed in 9.0 ml of an isotonic, pH buffered solution to make a working stock. An assay calls for .50 ml of this working stock to which is added .10 ml of serum. What is the cost of gold used for each test?
My work:
.10 % w/v gold = .10 g gold (in 1 ml)
(.10 g gold)/(1 ml + 9 ml) = .01% w/v gold (or .01 g gold)
(.01 g gold)/(1 ml) x (5 ml)/(1) = .005 g gold in final solution
.005 g gold x (1 troy ounce)/(33.8 g gold) = .0001479 troy ounces of gold in the final solution
.0001479 x $380 = about $.06 per test
Any guidance would be greatly appreciated. Thanks!
Sorry, in my 3rd step it should be "(.5ml)/(1)"
This is good, but mass/volume %= (g/mL)*100
So,
(0.10 % w/v)/100 = 0.001 g gold (in 1 ml)
And so,
(0.001g gold)/(1 ml + 9 ml) = 0.0001g of gold/mL
****Don't worry about mass/volume % at this point.
But now you have a solution that is 0.0001g of gold/mL
You remove 0.5mL of solution and add it to 0.10 mL of serum.
How much gold is in a total volume of 0.60 mL?
0.0001g of gold/mL *(0.10mL)=0.00001g of gold
Your new concentration will be
0.00001g of gold/total volume=0.00001g of gold/0.60mL=1.67 x 10^-5 g of gold/mL
or 1.67 x 10^-5 g of gold/mL*(100)=1.67 x 10^-3 % m/v
So, each test uses 0.00001g of gold
0.00001g of gold*(1 troy ounce)/(33.8 g gold) = 2.96 x 10^-7 troy ounces of gold in the final solution
(2.96 x 10^-7)* ($380/oz) = $1.12 x 10^-4
The test isn't that expensive.
Why did you multiply 0.0001g of gold/mL by 0.10mL? Shouldnt it be .50 mL? I say this because .10 is the volume of serum added, which does not contribute to the total amount of gold in the final solution.
Thank you for catching that.
0.0001g of gold/mL *(0.50mL)=0.00005g of gold
Your new concentration will be
0.00005g of gold/total volume=0.00005g of gold/0.60mL=8.33 x 10^-5 g of gold/mL
or 8.33 x 10^-5 g of gold/mL*(100)=8.33 x 10^-3 % m/v
So, each test uses 0.00005g of gold
0.00005g of gold*(1 troy ounce)/(33.8 g gold) = 1.48 x 10^-5 troy ounces of gold in the final solution
(1.48 x 10^-5)* ($380/oz) = $5.62 x 10^-3
Thanks for the help!
go back to basics and CHECK YOUR NUMBERS. There are only 31.1 grams in a troy ounce my friend...
Your calculation seems correct, but let me break it down to double-check. To find the cost of gold used for each test, we'll need to go step-by-step:
1. The concentration of the colloidal solution is given as 0.10% w/v, which means that there are 0.10 g of gold in 100 ml of the solution.
2. You took 1.0 ml of the colloidal solution and added it to 9.0 ml of the isotonic, pH buffered solution. This results in a total volume of 10.0 ml for the working stock solution.
3. To find the concentration of gold in the working stock solution, we divide the amount of gold by the total volume: 0.10 g / 10.0 ml = 0.01 g/ml = 0.01% w/v.
4. Next, you multiplied the concentration of gold by the volume of the assay: 0.01 g/ml x 0.5 ml = 0.005 g of gold in the final solution.
5. To convert grams to troy ounces, you used the conversion factor of 1 troy ounce = 33.8 g: 0.005 g / 33.8 g/troy ounce = 0.0001479 troy ounces of gold in the final solution.
6. Finally, you multiplied the amount of gold in troy ounces by the value of 1 troy ounce of gold which is $380: 0.0001479 troy ounces x $380 = approximately $0.06 per test.
Based on these calculations, it seems like you've correctly determined that the cost of gold used for each test is approximately $0.06. Well done!