Lab Report: Sedimentation, Absorption, and Osmosis

Abstract

The purpose of this lab was to analyze the process of sedimentation as viscous forces act upon particles in a liquid. Additionally, this lab aimed to observe the processes of absorption and osmosis. The sedimentation process was accelerated using a centrifuge to increase the acceleration due to gravity. The objective was to demonstrate that sedimentation involves particles falling through a viscous liquid at a constant velocity but not at a constant acceleration.

The main objective was to analyze the ratio of g_c/g both experimentally and theoretically in order to determine the percent error between the two values.

The theoretical value of g_c/g was determined to be 11, while the experimental value was determined to be 12. The percent error between the two values for g_c/g was calculated to be 9.1%.

Introduction

In this experiment, we aim to determine the centrifugal gravity (g_c) divided by the force of gravity (g) through both experimental and theoretical methods and compare them to calculate percent error.

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The percent error equation is as follows:

% Error = (|x_experimental - x_accepted|) / x_accepted × 100% (Equation 1)

The experimental determination of g_c/g will be obtained using the following equation:

g_c/g = (time-to-clear-at-g) / (time-to-clear-at-g_c) (Equation 2)

The theoretical value for g_c/g will be determined using:

g_c/g = (4π²R(RPM)²) / (3600 × 9.80) (Equation 3)

Where R is the distance from the center of the centrifuge to the center of the test tube (0.02 m) and RPM is the revolutions per minute (700 RPM).

The experimental velocity is determined by the graph plotting time versus clearing distance, and it can be calculated using the formula:

Rough determination of velocity (v):

v = m / (6πηr) (1 - ρ_f / ρ_m) g_c (Equation 4a)

Where m is the mass of a particle, η is the coefficient of viscosity (approximately 0.

001 Ns/m²), r is the radius of the tube (approximately 4×10⁻⁵ m), ρ_f is the density of the fluid (approximately 1000 kg/m³), and ρ_m is the density of the particles.

The relative mass of a particle (m) is determined using the momentum of the particle (ρ_m) in the following equation:

m = Volume of Tube × ρ_m (Equation 4b)

By substituting Equation 4b into Equation 4a, we obtain a simplified equation for velocity:

v = (2r²) / (9η(ρ_m - ρ_f)) g_c (Equation 4c)

Materials

• UV spectrometer
• Cow's blood
• Test tubes
• Sephacryl
• Stopwatch
• Ruler
• Centrifuge

Methods

The values of absorbance were determined using a spectrometer for three different mixtures: blood and pure water, blood and saltwater, and sephacryl. The data sets were graphed and analyzed.

To determine the experimental g_c/g ratio, a test tube of sephacryl was shaken up and placed upside down. The cleared distance was then measured from the meniscus to the top of the settling particles. Once the time to clear by the force of gravity was determined, the sephacryl tube was shaken again and placed inside the centrifuge, which was set to 700 RPMs. Multiple trials were conducted to determine the time required for all the sephacryl particles to settle to the bottom. This data was graphed to determine velocity.

Results

In this lab, absorbance data was collected using a UV spectrometer for three test tubes containing different mixtures: blood and pure water, blood and saltwater, and sephacryl. The following data was obtained:

Table 1: Blood and Pure Water Absorbance vs. Wavelength

Table 2: Blood and Salt Water Absorbance vs. Wavelength

Table 3: Sephacryl Absorbance vs. Wavelength

When analyzing the graphs, it is evident that the blood and saltwater mixture had a much higher absorbance than the pure water and blood mixture. This higher absorbance is due to the cells being isotonic in the saltwater mixture, while the pure water was hypotonic, causing the cells to lyse. Lysed cells result in a solution containing proteins and lipids, tinting the solution red but still allowing light to pass through easily. The saltwater mixture, on the other hand, contains intact cells that absorb most of the light. In both cases, absorbance decreases around the 600nm range, which corresponds to the red light wavelength, as hemoglobin reflects red light, giving it a red color. Sephacryl showed little to no absorbance compared to the other mixtures, indicating scattering.

When working with sephacryl, the goal is to determine the components of viscous forces acting in the sedimentation process. The ratio of g_c/g was determined by measuring the time to clear at 1 g and at the force of gravity created in the centrifuge. The time to clear in the centrifuge was found to be 120 s, while the time to clear at normal gravity was 1450 s. These values were used in Equation 2 to calculate g_c/g:

g_c/g = (1450 s) / (120 s) = 12

The experimentally determined value for g_c/g is 12.

To determine the theoretical value of g_c/g, Equation 3 was used:

g_c/g = (4π²R(RPM)²) / (3600 × 9.80)

Substituting the values: R = 0.02 m and RPM = 700 RPM,

g_c/g = (4π²(0.02 m)(700 RPM)²) / (3600 × 9.80) = 11

The theoretical value of g_c/g is 11.

The percent error between the experimental and theoretical values for g_c/g was calculated using Equation 1:

% Error = (|12 - 11|) / 11 × 100% = 9.1%

The percent error in the experimental to theoretical values for g_c/g was determined to be 9.1%.

Velocity was determined from the graphed data of sedimentation of sephacryl clearance versus time (Graph 4). The velocity was found to be (5 × 10⁻⁵ ± 2 × 10⁻⁶) m/s.

Using velocity, the density of the particles was calculated with Equation 4c, assuming a velocity value of 0.6 for accuracy:

v = (2r²) / (9η(ρ_m - ρ_f)) g_c

Substituting values:

(5 × 10⁻⁵ m/s) = (2(4 × 10⁻⁵ m)²) / (9(0.001 Ns/m²)(ρ_m - 1000 kg/m³)(9.80 m/s²))

((5 × 10⁻⁵) / (3.56 × 10⁻⁷)) / 9.80 = ρ_m - 1000 kg/m³

14.35 + 1000 kg/m³ = ρ_m

ρ_m = 1014 kg/m³

The density of the particles was determined to be 1014 kg/m³.

Discussion

The experimentally determined value for g_c/g was calculated to be 12, while the theoretical value was calculated to be 11. The percent error between the experimental and theoretical values for g_c/g was found to be 9.1%. Several sources of error could contribute to this discrepancy, with the most likely sources being the estimation of values for R and time-to-clear-at-g_c. Accurately measuring the distance R was challenging due to the centrifuge rotor's obstruction. Determining the time to clear in the centrifuge could have been more precise with additional trials to obtain a more accurate time for complete sedimentation.

One aspect that deserves more attention in this lab is the osmosis portion. Osmosis is a critical concept in biology and medicine, and it connects chemistry, biology, and physics. Given the relevance of osmosis to biology and pre-medical studies, it would be beneficial to emphasize and explain the osmosis process more comprehensively in this lab.