Self-test Key

Abstract

• 1. 90 s. Time constant (15 s) × six = response time. Refer to Sect. 1.

• 2. The enthalpy change, Δ_rH, for the first reaction is (2.0 J/0.038 mmole) = −52 J/mmole or −52 kJ/mole. Δ_rH for the second reaction is 0 kJ/mole. Δ_rH for dilution of the titrant is (−0.1 J/0.021 mmole) = +4.8 kJ/mole. Amines are usually more basic than carboxylates, so the expectation is that the amine is the first reaction, but the proof is the Δ_rH value, −50 kJ/mole is a defining characteristic for protonation of amines, and 0 kJ/mole is a defining characteristic of protonation of carboxylate groups. The mole ratio of amine to carboxylate is (0.038/0.041) = 0.93. Refer to Sect. 3.9.

• 3. The stoichiometry is three stronger binding sites and four weaker binding sites. Both kinds of sites are cooperative, i.e., K1 ≈ K2 ≈ K3 < K4 ≈ K5 ≈ K6 ≈ K7. The enthalpy change, Δ_rH, for the strong binding site is −50 kJ/mole and for the weaker binding site, −30 kJ/mole. The rounded endpoints show that the binding constants β₃ and β_4–7 could be calculated from these data. Refer to Sects. 2, 3.4, 3.8, and 5.

• 4. The concentration of nitrite is 59 μM. (11.21 J/°C)(0.0053 °C) = 0.0594 J; (0.0594 J)/(−402,000 J/mol)) = 0.1478 μmols product; 1:1 relationship, so the concentration is (0.1478)/(2.5 mL) = 59 μM. There is a large excess of sulfamic acid, i.e., (0.05 M)(10⁶ μmole/mole)(10⁻³ L/mL)(0.15 mL) = 7.5 μmoles. The temperature measurement limits the answer to two significant digits. Refer to Sect. 3.3.

• 5. One H⁺ released. The reactions are