Just..... don't get it
A column packing for chromatography consists of a mixture of two types of particles. Assume that the particles in the batch being sampled are spherical with a radius of 0.5 mm. 36% of the particles appeared to be pink and are known to have a polymeric stationary phase attached. The average density of the mixture is 0.288 g cm-3. If 5.3126(+/-)0.0003 g of the sample is weighed out, calculate,
(i) the number of particles in the sample
(ii) the % standard deviation in sampling the fraction of pink particles from this mass of the sample.
(iii) Which contributes the larger uncertainty to the procedure - weighing out the sample or the random error associated with sampling from the two-component mixture? Justify your answer with a calculation.
(iv) Assume that the % standard deviation in sampling is 8%. How many replicate samples of this packing material need to be taken so that there is 95% confidence that the mean is known to within „b6% of the true mean.
plz helppp
To answer these questions, we need to break down the problem step by step.
(i) To calculate the number of particles in the sample, we need to use the formula:
Number of particles = Mass of the sample / Mass of one particle
Given:
- Mass of the sample = 5.3126 ± 0.0003 g
- Radius of the particle = 0.5 mm
First, let's convert the radius to centimeters:
Radius = 0.5 mm = 0.05 cm
Next, we can calculate the volume of one particle using the formula for the volume of a sphere:
Volume of one particle = (4/3) * π * (radius)^3
Now, we can calculate the mass of one particle using the average density of the mixture:
Mass of one particle = Volume of one particle * Average density
Finally, we can calculate the number of particles using the formula mentioned earlier:
Number of particles = Mass of the sample / Mass of one particle
(ii) To calculate the % standard deviation in sampling the fraction of pink particles, we need to know the expression for standard deviation. However, it is not provided in the question. This information is necessary to answer this part.
(iii) To determine which contributes more uncertainty - weighing out the sample or the random error associated with sampling - we need to compare the relative standard deviations of each component.
The relative standard deviation for weighing out the sample can be calculated using the formula:
Relative Standard Deviation (%) = (Standard deviation / Mean) * 100
For the random error associated with sampling, we need the standard deviation (from part ii) and divide it by the fraction of pink particles.
(iv) To determine the number of replicate samples needed for 95% confidence, we can use the formula for the margin of error:
Margin of error = Critical value * (Standard deviation / sqrt(n))
Here, we are given the % standard deviation (8%) and the desired confidence level (95%). The critical value can be obtained from a standard normal distribution table based on the confidence level. The margin of error is set to 6% of the true mean.
Using the margin of error formula, we can solve for the required number of replicate samples (n).