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
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.
Well, I found the post by R_Scott. His two equations make for a much simpler process than the two I set up.
No problem! I'll be happy to guide you through the steps to solve this problem.
Step 1: Understand the problem and given information
You have 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, and you are given the densities of gold (19.3 g/cm^3) and silver (10.5 g/cm^3).
Step 2: Calculate the volume of silver in the jewelry
Since we know the total volume of the jewelry is the sum of the volumes of gold and silver, we can subtract the volume of gold from the total volume to find the volume of silver.
Volume of silver = Total volume - Volume of gold
Volume of silver = 0.685 cm^3 - Volume of gold
Step 3: Calculate the volume of gold in the jewelry
Since the density of gold is given, we can use the formula:
Mass = Density x Volume
Mass of gold = Density of gold x Volume of gold
Mass of gold = 19.3 g/cm^3 x Volume of gold
To convert the mass of gold to the volume of gold, we can use its density:
Mass = Density x Volume
Volume of gold = Mass of gold / Density of gold
Volume of gold = Mass of gold / 19.3 g/cm^3
Step 4: Substitute the given values into the equations
- From Step 2: Volume of silver = 0.685 cm^3 - Volume of gold
- From Step 3: Volume of gold = Mass of gold / 19.3 g/cm^3
Step 5: Solve for the volume of silver
Substitute the value of Volume of gold from Step 3 into the equation from Step 2 to solve for the volume of silver:
Volume of silver = 0.685 cm^3 - (Mass of gold / 19.3 g/cm^3)
Step 6: Calculate the mass of silver
Mass of silver can be calculated by multiplying the volume of silver by the density of silver:
Mass of silver = Density of silver x Volume of silver
Mass of silver = 10.5 g/cm^3 x Volume of silver
Step 7: Calculate the mass percentage of gold in the jewelry
The mass percentage of gold can be calculated using the formula:
Percentage of gold = (Mass of gold / Total mass) x 100
Total mass = Mass of gold + Mass of silver
By substituting the values obtained in Step 3 and Step 6 into the formula for Percentage of gold, you can calculate the desired result.
Remember to carefully plug in each value into the appropriate equation and perform the necessary calculations at each step to arrive at the final answer. If you encounter any specific difficulties during the calculations, feel free to ask for further clarification.