Answer: Two-step dilution; 0.0014
Explanation:
from the question, we would be defining the parameters given.
Step 1 : consider that 10-mL transfer pipet and a 1000-mL volumetric flask is to be used.
Step 2 : 50-mL pipet and a 1000-mL volumetric flask for the first dilution, and a 100-mL pipet and a 500-mL volumetric flask is used.
given that the pipe used are 10-ml, 50-ml and 100-ml.
From the textbook on tolerance of glassware,
the tolerance at 10-ml pipet = 0.03ml
for 50-ml pipet = 0.05ml
for 100-ml pipet = 0.08ml
for 500-ml volumetric flask = 0.2ml
for 1000-ml volumetric flask = 0.3ml
from step 1, the ratio of concentration is given as = P1/F1 = 10ml/1000ml = 0.01
while that of step 2 is given as = P1/F1 × P2/F2 = 50/1000 × 100/500 = 0.01
∴ the smallest overall relative uncertainty (Error) = σc/c
σc/c = √ (Σ (σPtl/Pp)² + Σ (σFtl/Fp)²) ......................... (1)
from step 1, applying the error formula we have;
σc/c (₁) = √ ( (0.03/10)² + (0.3/1000)²) = 0.003015 = 3.015 × 10⁻³
also step 2, σc/c (₂) = √ (0.05/50)² + (0.08/100)² + (0.03/1000)² + (0.2/500)²
= 0.0014 = 1.4 × 10⁻³
comparing values, we have that σc/c (₂) ˃ ˃ σc/c (₁) which means that the two dilution step of 0.0014 has the smallest relative uncertainty (error).
the value here is 1.4 × 10⁻³