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Chapter 11: Problem 90

An aqueous solution of \(10.00 \mathrm{~g}\) of catalase, an enzyme found in the liver, has a volume of \(1.00 \mathrm{~L}\) at \(27^{\circ} \mathrm{C}\). The solution's osmotic pressure at \(27^{\circ} \mathrm{C}\) is found to be \(0.745\) torr. Calculate the molar mass of catalase.

Short Answer

Expert verified
The molar mass of catalase is approximately \(2.52 * 10^5 \mathrm{~g/mol}\).

Step by step solution

01

Convert temperature to Kelvin and pressure to atm

First, we need to convert the given temperature of 27°C to Kelvin. We do this by adding 273.15. T = 27 + 273.15 = 300.15 K Next, we need to convert the osmotic pressure from torr to atm. We use the conversion factor: 1 atm = 760 torr Π = 0.745 torr * (1 atm / 760 torr) = 0.0009796 atm
02

Rearrange the osmotic pressure formula to find the number of moles (n)

Now we will rearrange the osmotic pressure formula to find the number of moles (n): n = (Π * V) / (R * T) Where V is the volume (1.00 L), R is the ideal gas constant (0.0821 L atm/mol K), and T is the temperature (300.15 K).
03

Calculate the number of moles (n) of catalase

Now plug in the values for Π, V, R, and T to calculate the number of moles: n = (0.0009796 atm * 1.00 L) / (0.0821 L atm/mol K * 300.15 K) n ≈ 3.97 * 10^-5 mol
04

Calculate the molar mass (M) of catalase

Now that we have the number of moles, we can find the molar mass (M) of catalase using the formula: M = mass / n Where mass is the mass of catalase (10.00 g) and n is the number of moles (3.97 * 10^-5 mol). M = 10.00 g / (3.97 * 10^-5 mol) ≈ 2.52 * 10^5 g/mol The molar mass of catalase is approximately 2.52 * 10^5 g/mol.

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Most popular questions from this chapter

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 (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 \(25.0^{\circ} \mathrm{C} ?\)

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In some regions of the southwest United States, the water is very hard. For example, in Las Cruces, New Mexico, the tap water contains about \(560 \mu \mathrm{g}\) of dissolved solids per milliliter. Reverse osmosis units are marketed in this area to soften water. A typical unit exerts a pressure of \(8.0 \mathrm{~atm}\) and can produce \(45 \mathrm{~L}\) water per day. a. Assuming all of the dissolved solids are \(\mathrm{MgCO}_{3}\) and assuming a temperature of \(27^{\circ} \mathrm{C}\), what total volume of water must be processed to produce \(45 \mathrm{~L}\) pure water? b. Would the same system work for purifying seawater? (Assume seawater is \(0.60 \mathrm{M} \mathrm{NaCl}\).)
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