A 50.0 g of an enzyme was dissolved in water to give 2600 mL solution at 30.0 oC. The osmotic pressure resulting solution was found to be 0.0048 atm. Calculate the molecular weight of an enzyme (R = 0.0821 mol.K. L-1. atm-1).
May 29, 2024To calculate the molecular weight of the enzyme, we can use the equation for osmotic pressure: π = MRT Where: π = osmotic pressure M = molarity of the solution (in mol/L) R = ideal gas constant (0.0821 L.atm/mol.K) T = temperature (in Kelvin) First, let's calculate the molarity of the enzyme solution using the given mass and volume. Step 1: Calculate the molarity (M) Convert the volume from mL to L: 2600 mL = 2.6 L Molarity (M) = moles of solute / liters of solution Moles of solute = mass of enzyme / molar mass of enzyme We need to find the moles of the enzyme to calculate its molar mass. So, first, we calculate the moles of the enzyme. Mass of enzyme = 50.0 g Moles of enzyme = mass / molar mass Moles of enzyme = 50.0 g / molar mass Now, let's apply the ideal gas equation: π = MRT (we are calculating M) Rearranging the equation: M = π / RT Step 2: Plug in the values and solve for M π = 0.0048 atm (osmotic pressure) R = 0.0821 L.atm/mol.K (ideal gas constant) T = 30.0 + 273.15 K (temperature converted to Kelvin) M = 0.0048 atm / (0.0821 L.atm/mol.K * 303.15 K) M = 0.0048 atm / 24.855 L mol^-1 M ≈ 0.000193 mol/L Now we know the molarity of the enzyme solution, we can calculate the molar mass. Step 3: Calculate the molar mass Molar mass of the enzyme = Mass / Moles Molar mass = 50.0 g / 0.000193 mol Molar mass ≈ 259.6 g/mol So, the molecular weight of the enzyme is approximately 259.6 g/mol.
May 29, 2024To calculate the molecular weight of the enzyme, we can use the formula for osmotic pressure: π = MRT Where: π = osmotic pressure (0.0048 atm) M = molarity of the solution (moles/L) R = gas constant (0.0821 L.atm/mol.K) T = temperature in Kelvin (273 + 30 = 303 K) First, we need to calculate the molarity of the solution: Molarity (M) = moles of solute / liters of solution Given that there are 50.0 g of the enzyme in 2600 mL of solution, we need to convert grams to moles: Moles = mass / molar mass The molar mass of the enzyme is given by: Molar mass = (mass of enzyme) / (moles of enzyme) Now, let's calculate the moles of the enzyme: Moles = 50.0 g / Molar mass Next, convert 2600 mL to liters: Liters = 2600 mL / 1000 = 2.6 L Now, calculate the molarity: Molarity = moles / liters Now we can substitute these values into the osmotic pressure formula: 0.0048 atm = (moles / 2.6 L) * 0.0821 L.atm/mol.K * 303 K Solve for moles: moles = (0.0048 atm * 2.6 L) / (0.0821 L.atm/mol.K * 303 K) Once you have calculated moles, you can use this value to determine the molecular weight of the enzyme using the molar mass formula.
May 29, 2024
Chatgpt ትውልድ
May 29, 2024To calculate the molecular weight of the enzyme, we can use the formula for osmotic pressure, which is given by: \[ \Pi = \frac{n}{V}RT \] where: - \(\Pi\) is the osmotic pressure, - \(n\) is the number of moles of the solute, - \(V\) is the volume of the solution in liters, - \(R\) is the ideal gas constant, - \(T\) is the temperature in Kelvin. We can rearrange this formula to solve for the molecular weight \(M\) of the enzyme: \[ \Pi = \frac{m}{M \cdot V}RT \] where \(m\) is the mass of the solute. Rearranging for \(M\): \[ M = \frac{mRT}{\Pi V} \] Given the data: - \(m = 50.0 \text{ g}\) - \(\Pi = 0.0048 \text{ atm}\) - \(V = 2600 \text{ mL} = 2.6 \text{ L}\) - \(T = 30.0 \degree \text{C} = 303.15 \text{ K}\) - \(R = 0.0821 \text{ L atm K}^{-1} \text{ mol}^{-1}\) Plugging in the values: \[ M = \frac{50.0 \text{ g} \times 0.0821 \text{ L atm K}^{-1} \text{ mol}^{-1} \times 303.15 \text{ K}}{0.0048 \text{ atm} \times 2.6 \text{ L}} \] Let's calculate this step-by-step. 1. Calculate the numerator: \[ 50.0 \times 0.0821 \times 303.15 = 1245.15675 \text{ g atm K} \text{ mol}^{-1} \] 2. Calculate the denominator: \[ 0.0048 \times 2.6 = 0.01248 \text{ atm L} \] 3. Divide the numerator by the denominator: \[ M = \frac{1245.15675}{0.01248} \approx 99779.26 \text{ g/mol} \] Therefore, the molecular weight of the enzyme is approximately \( 99779.26 \text{ g/mol} \).
May 29, 2024