The specific rotations of the α and β anomers of D-glucose are +112 degrees and +18.7...

The specific rotations of the α and β anomers of D-glucose are +112 degrees and +18.7 degrees, respectively. Specific rotation, [α]D, is defined as the observed rotation of light of wavelength 589 nm (the D line of a sodium lamp) passing through 10 cm of a 1 g/mL solution of a sample. When a crystalline sample of α-D-glucose is dissolved in water, the specific rotation decreases from 112 degrees to an equilibrium value of 52.7 degrees. On the basis of this result, what are the proportions of α and β anomers at equilibrium? Assume the concentration of the open-chain form is negligible.

Expert Solution

queen_honey_blossom answered 2 years ago

A = [(α −β −β), (−β α −β), (−β −β α) ] (each row is in...

A = [(α −β −β), (−β α −β), (−β −β α) ] (each row is in paranthesis) (c) Find the algebraic multiplicity and the geometric multiplicity of every eigenvalue of A. (d) Justify if the matrix A is diagonalizable.

The enzyme glucose oxidase isolated from the mold Penicillium notatum catalyzes the oxidation of β-D-glucose to...

The enzyme glucose oxidase isolated from the mold Penicillium notatum catalyzes the oxidation of β-D-glucose to D-glucono-δ-lactone. This enzyme is highly specific for the β anomer of glucose and does not affect the α anomer. In spite of this specificity, the reaction catalyzed by glucose oxidase is commonly used in a clinical assay for total blood glucose –that is, for solutions consisting of a mixture of β-D-glucose and α-D-glucose. What makes it possible for this test to measure total blood...

Let α, β be cuts as defined by the following: 1) α ≠ ∅ and α...

Let α, β be cuts as defined by the following: 1) α ≠ ∅ and α ≠ Q 2) if r ∈ α and s ∈ Q satisfies s < r, then s ∈ α. 3) if r ∈ α, then there exists s ∈ Q with s > r and s ∈ α. Let α + β = {r + s | r ∈ α and s ∈ β}. Show that the set of all cuts R with the...

A firm’s production function is ? = ?Lα ?β where A, α, and β are positive...

A firm’s production function is ? = ?Lα ?β where A, α, and β are positive constants. The firm currently uses 500 units of labor and 40 units of capital. If the firm adds 1 more unit of labor, what happens to productivity of capital? Explain. Given a production function Q = f(L, K), if marginal product of labor and marginal product of capital are both positive, then this function displays diminishing MRTS. Explain if this statement is true or...

Consider the model Et = α + β It + ut

Consider the model Et = α + β It + ut where ut has a zero mean Where Et is aggregate expenditure on a good and It is total income. Given the following information OLS Estimates Using 51 Observations Dependent Variable Et Variable Coeff STD error T Stat constant 0.26644 0.3294 .809 It 0.06754 .0035 19.288 SSR = 157.90709 Unadjusted R2 = 0.884 Adjusted R2 = .881 OLS Estimates Using 51 Observations Dependent Variable u2t...

1. Homework 4 Due: 2/28 Let X1,...,Xn i.i.d. Gamma(α,β) with α > 0, β > 0...

1. Homework 4 Due: 2/28 Let X1,...,Xn i.i.d. Gamma(α,β) with α > 0, β > 0 (a) Assume both α and β are unknown, find their momthod of moment estimators: αˆMOM and βˆMOM. (b) Assume α is known and β is unknown, find the maximum likelihood estimation for β. 2.

If sec(α) = − 13 5 where π 2 < α < π and tan(β) =...

If sec(α) = − 13 5 where π 2 < α < π and tan(β) = 24 7 where π < β < 3π 2 , find the exact values of the following. (a) csc(α − β) (b) sec(α + β) (c) cot(α + β)

1.The specific rotation, [α]D, for (-)-malic acid is -27. What is the observed rotation for a...

1.The specific rotation, [α]D, for (-)-malic acid is -27. What is the observed rotation for a solution of 0.50 g of (-)-malic acid in 10 mL of water in a sample tube having a pathlength of 10 cm? B) The observed rotation of a solution of 1.3 g of a compound in 10 mL of water is +11 degrees. If the pathlength is 10 cm, what is the specific rotation of the compound? 2. The specific rotation, [α]D, for (-)-2-butanol...

The specific rotation, [α]D, for (-)-2-butanol is +14. What is the observed rotation for a solution...

The specific rotation, [α]D, for (-)-2-butanol is +14. What is the observed rotation for a solution of 1.0 g of (-)-2-butanol in 10 mL of water in a sample tube having a pathlength of 10 cm? ??????degrees . The observed rotation of a solution of 1.5 g of a compound in 10 mL of water is +3.4 degrees. If the pathlength is 10 cm, what is the specific rotation of the compound? .

The specific rotation, [α]D, for (-)-malic acidis -27. What is the observed rotation for a solution...

The specific rotation, [α]D, for (-)-malic acidis -27. What is the observed rotation for a solution of 0.75 g of (-)-malic acid in 10 mL of water in a sample tube having a pathlength of 10 cm? The observed rotation of a solution of 1.4 g of a compound in 10 mL of water is -10degrees. If the pathlength is 10 cm, what is the specific rotation of the compound? The specific rotation, [α]D, for (-)-malic acidis -27. What is...

Question