I tried to find your original post and can't find it; therefore, I can't find the solutions R_Scott and oobleck gave to you although I remember they did give you the equations. It would have been helpful if you had reposted the two solutions. I will try to duplicate the one by R_Scott but I don't know that I can do that.
You have two equations and you are to solve them simultaneously.
Equation 1 is this.
Let G = mass Au and S = mass silver. How much does the jewelry weight. It's 9.50 grams so
eqn 1 is G + S = 9.50 g
Next you know the volume is 0.685 cc and the problem is assuming the volumes are additive; therefore, volume Au + volume Ag = 0.685. So what is the volume? That's mass = volume x density or V = mass/density You know the densities.
V Gold = mass gold/density gold = G/19.3
V Silver = mass silver/density silver = S/10.5
sol the second equation is G/19.3 + S/10.5 = 0.685
Here are the two equations which I've labeled.
(1)............G + S = 9.50
(2)........G/19.3 + S/10.5 = 0.685
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First let's make (2) look better by getting rid of the denominators. Do that by multiplying by 10.5 x 19.3 like this:
[(19.3*10.5)G/19.3] + [(19.3*10.5)S/10.5] = 19.3*10.5*0.685
19.3 in the first term and 10.5 in the second term cancels and we have
10.5G + 19.3S = 19.3*10.5*0.685 or
10.5G + 19.3S = 138.82
You now have two equations in two unknowns and you solve them simultaneously.
Take equation 1 and solve for S.
(1)...........G + S = 9.50 g
so S = 9.50 - G and substitute this into the new equation 2 like this.
equation 2 is 10.5G + 19.3S = 138.82
Placing S in equation 2 like this gives you
10.5G + 19.3(9.50-G) = 138.82. You see this gets rid of S this way and you have only one unknown, namely G or mass Gold.
Solve that equation which gives you mass gold, then
% Au = (mass Au/mass sample)*100 = ?
I hope this helps.
Consider a piece of gold jewelry that weighs 9.50 g and has a volume of 0.685 cm^3 . The jewelry contains only gold and silver, which have densities of 19.3 g/cm^3 and 10.5 g/cm^3, respectively. If the total volume of the jewelry is the sum of the volumes of the gold and silver that it contains, calculate the percentage of gold (by mass) in the jewelry.
I have been given the equation of how to do this, but I don't even know where to start with plugging in the values. Can someone walk me through these steps? It is almost 12:40 where I am and I have 29 more after this one and I have been stuck on It for 30 mins because I missed class today
2 answers
Well, I found the post by R_Scott. His two equations make for a much simpler process than the two I set up.