To determine the density of block of aluminum, you measured the mass at 101.1 g and a volume of 38.2 cm3 . When you looked up the value for aluminum density you found out it should be 2700 kg/m3 What is the percent error for your experimental data?
a) 1.98%
c) 19.8%
b) 0.198 %
d) cannot determine
101.1g = 0.1011kg,
V = 10^-6m^3/cm^3 * 38.2cm^3 =
38.2*10^-6m^3.
Density = 0.1011kg / 38.2*10^-6m^3 =
2.6466*10^-3 * 10^6 = 2647kg/m^3.
Error = 2700 - 2647 = 53kg/m^3.
%Error = (53/2700) * 100% = 1.96.
ans. = a.
To determine the percent error, you need to compare your experimental data with the accepted value. The formula for percent error is:
Percent Error = (|Experimental Value - Accepted Value| / Accepted Value) * 100%
In this case, your experimental value for the density of aluminum is determined by dividing the mass by the volume: 101.1 g / 38.2 cm^3.
To proceed with the calculation, we need to ensure that the units are consistent. Since the accepted value for aluminum density is given in kg/m^3, we need to convert the experimental value to the same units.
To convert the experimental value, we need to convert grams to kilograms and cubic centimeters to cubic meters. There are 1000 grams in a kilogram and 100 centimeters in a meter, so:
Experimental Value (in kg/m^3) = (101.1 g / 1000) / (38.2 cm^3 / (100^3))
Simplifying the units, we have:
Experimental Value (in kg/m^3) = 0.1011 kg / 0.0000382 m^3
Now, we can calculate the percent error:
Percent Error = (|0.1011 kg/m^3 - 2700 kg/m^3| / 2700 kg/m^3) * 100%
Calculating the absolute difference in densities:
|0.1011 kg/m^3 - 2700 kg/m^3| = 2699.8989 kg/m^3
Plugging in the values:
Percent Error = (2699.8989 kg/m^3 / 2700 kg/m^3) * 100%
Simplifying:
Percent Error = 0.999962% ≈ 1.00%
So, the correct answer is option a) 1.98%.