Question

Creatinine, \(\mathrm{C}_{4} \mathrm{H}_{7} \mathrm{N}_{3} \mathrm{O}\) , is a by-product of muscle metabolism, and creatinine levels in the body are known to be a fairly reliable indicator of kidney function. The normal level of creatinine in the blood for adults is approximately 1.0 \(\mathrm{mg}\) per deciliter \((\mathrm{dL})\) of blood. If the density of blood is 1.025 \(\mathrm{g} / \mathrm{mL}\) , calculate the molality of a normal creatinine level in a \(10.0-\) \(\mathrm{mL}\) blood sample. What is the osmotic pressure of this solution at \(25.0^{\circ} \mathrm{C} ?\)

Short answer

The molality of a normal creatinine level in a 10.0 mL blood sample is approximately \(8.61 \times 10^{-5}\) mol/kg. The osmotic pressure of this solution at 25.0°C is approximately 0.0215 Pa.

Step-by-step solution

Convert the given information into the required units

We start by converting 10.0 mL blood sample to mass and 1.0 mg/dL creatinine level to moles. Density of blood = 1.025 g/mL Mass of blood = Density × Volume = 1.025 g/mL × 10.0 mL = 10.25 g 1 dL = 100 mL Creatinine level = 1.0 mg/dL = 0.01 mg/mL Mass of creatinine in the blood sample = 0.01 mg/mL × 10.0 mL = 0.1 mg Given that the molar mass of creatinine (C\(_4\)H\(_7\)N\(_3\)O) is roughly M = 113.12 g/mol. Now we will convert the mass of creatinine in our sample from mg to g: Mass of creatinine = 0.1 mg × (1 g/1000 mg) = 0.0001 g Now we will convert grams of creatinine to moles using its molar mass: Moles of creatinine = Mass / Molar mass = 0.0001 g / 113.12 g/mol = 8.83 × 10\(^{-7}\) mol

Calculate molality of the solution

Now that we have the moles of creatinine in the blood sample, we can calculate the molality. The formula for molality is: Molality = Moles of solute / Mass of solvent (in kg) In our case, the solute is creatinine and the solvent is blood. Molality = 8.83 × 10\(^{-7}\) mol / 0.01025 kg = 8.61 × 10\(^{-5}\) mol/kg

Calculate the osmotic pressure of the solution

Now we will calculate the osmotic pressure of the solution using the following formula: Osmotic pressure (π) = n × R × T where n = molality of the solution = 8.61 × 10\(^{-5}\) mol/kg R = gas constant = 8.314 J/mol·K (since we are using SI units) T = temperature in Kelvin = 273.15 + 25.0 = 298.15 K We can now plug in these values into the osmotic pressure formula: Osmotic pressure (π) = 8.61 × 10\(^{-5}\) mol/kg × 8.314 J/mol·K × 298.15 K = 0.0215 Pa The osmotic pressure of this solution at 25.0°C is approximately 0.0215 Pa.

Key concepts

Muscle Metabolism

During physical activities, our muscles burn energy through a process called metabolism. One crucial by-product of this process is creatinine, a compound that is released into the bloodstream.
Creatinine formation happens when creatine, a component involved in producing energy for muscle contractions, breaks down. This breakdown is a part of a natural metabolic cycle in muscles.
Most creatinine is produced at a constant rate and its levels are relatively stable, reflecting a consistent turnover in muscle metabolism. It does not really fluctuate based on exercise or diet, which helps in using it as a reliable measure in medical diagnostics.

Kidney Function Indicators

Creatinine levels in the blood serve as a vital indicator for kidney health. Since creatinine is filtered out of the blood by the kidneys and excreted in urine, doctors can use its concentration to gauge how well the kidneys are working.

• Normal creatinine levels suggest healthy kidney function.
• Elevated levels might indicate impaired kidney function. This could mean that kidneys are not effectively disposing of waste.
• Creatinine clearance tests measure how quickly creatine is removed from the bloodstream, helping further assess kidney performance.

Regular monitoring of creatinine can be crucial for early diagnosis and management of kidney-related conditions.

Blood Chemistry

Blood chemistry involves analyzing various substances within the bloodstream, including electrolytes, gases, proteins, and waste products like creatinine.
Here, the focus is on understanding the concentration levels of these substances to ensure that they fall within the normal range, ensuring the body's homeostasis.
Since blood serves as a transport medium throughout the body:

• Changes in concentration levels can highlight issues such as dehydration, kidney disease, metabolic disorders, and more.
• Understanding the chemical composition of blood is crucial for diagnosing diseases."
• The density and volume of the blood must be considered when calculating the concentrations, as shown in the exercise when calculating molality.

Osmotic Pressure Calculation

Osmotic pressure is a concept tied to the movement of molecules through a semipermeable membrane due to differences in solute concentration on each side.

The pressure determines the tendency of solvent molecules, like water, to move into an area of higher solute concentration. In the context of blood, this influences how water moves across cell membranes, impacting fluid balance in the body.

• The formula: \[ \pi = nRT \] where \( n \) is molality, \( R \) is the universal gas constant, and \( T \) is temperature in Kelvin.
• Applying this to our blood sample allows us to determine the osmotic pressure, essential for understanding fluid dynamics in bodily systems.
• Miscalculations can lead to undesirable conditions such as cells swelling or shrinking.

Understanding osmotic pressure is critical in many physiological and pathological conditions.