Question

The density of an object is calculated by measuring its mass with a scale (s=±0.0001 g) and measuring its volume by volume displacement in a graduated cylinder (s=±0.1 mL). Mass = 41.6225 g Initial volume = 6.30 mL Final volume = 22.70 mL Calculate the density and express the answer including the error in the calculation.

Please indicate units and correct Significant Figures

Answer 1

Initial volume = 6.30 mL.

Final volume = 22.70 mL.

Volume displaced = volume of the object = (22.70 – 6.30) mL = 16.40 mL.

Uncertainty in the mass of the object, U_m = Δm/m = (0.0001 g)/(41.6225 g) = 2.4025*10^-6

Uncertainty in the volume of the object, U_V = ΔV/V = (0.1 mL)/(16.40 mL) = 6.0976*10^-3.

Density of the object = (mass of the object)/(volume of the object)

= (41.6225 g)/(16.40 mL) = 2.5379 g/mL ≈ 2.538 g/mL

Uncertainty in the density of the object, U_d = Δd/d = √(2.4025*10^-6)² + (6.0976*10^-3)² = 6.0976*10^-3

Absolute uncertainty in the density of the object = d*U_d = (2.5379 g/mL)*(6.0976*10^-3) = 0.01547 g/mL ≈ 0.0155 g/mL.

The measured density of the object is 2.5380.0155 g/mL (ans, correct to four sig. figs).