A gold nugget that weighs 20.053 g on the balance is lowered into a graduated cylinder filled with ethanol. If the initial ethanol level was 10.10 mL, what will the final ethanol level be?
You will need the density of Au, then
volume = mass/density
Substitute mass from the problem and density you have to find volume.
Then volume Au + 10.10 mL = new volume of the ethanol in the graduated cylinder.
1.04 g/mL
To determine the final ethanol level after lowering a gold nugget into a graduated cylinder filled with ethanol, we need to use the principle of displacement. The gold nugget will displace a certain volume of ethanol equal to its own volume.
To solve this problem, we need the density of gold, which we can find either from a reference table or by searching online. The density of gold is approximately 19.3 g/cm³.
Given that the gold nugget weighs 20.053 g, we can calculate its volume by dividing its weight by its density:
Volume of gold nugget = Weight of gold nugget / Density of gold
Volume of gold nugget = 20.053 g / 19.3 g/cm³
Now, let's substitute the given values into the equation:
Volume of gold nugget = 20.053 g / 19.3 g/cm³
Volume of gold nugget ≈ 1.039 cm³
Since the volume of gold nugget is equal to the volume of ethanol displaced, the final ethanol level, or the volume of ethanol, will increase by 1.039 mL. Therefore, the final ethanol level will be the initial ethanol level plus the volume of ethanol displaced:
Final ethanol level = Initial ethanol level + Volume of ethanol displaced
Final ethanol level = 10.10 mL + 1.039 mL
Calculating this sum:
Final ethanol level ≈ 11.139 mL
Hence, the final ethanol level will be approximately 11.139 mL.