Answer:
Explanation:
Assuming all calculations occur at standard pressure and a temperature of -1.72°C :
Where
is the number of moles of hydrogen
is the mass of hydrogen
is the density of hydrogen
The change in temperature can be expressed as:
By substituting in the known values, we arrive at:
Thus, we obtain the required answer.
1) The ionic compound present in solution b is K₂CrO₄ (potassium chromate). This compound contains two potassiums (oxidation state +1), a single chromium (oxidation state +6), and four oxygen atoms. The oxidation state of oxygen is -2, resulting in a neutral compound: 2 · (+1) + 6 + x · (-2) = 0. Hence, x = 4, denoting the count of oxygen atoms. 2) The ionic compound in solution a is AgNO₃ (silver nitrate). ω(N) = 8.246% ÷ 100%. Thus, ω(N) = 0.08246, indicating the mass percentage of nitrogen. M(MNO₃) = M(N) ÷ ω(N). It follows that M(MNO₃) = 14 g/mol ÷ 0.08246, leading to M(MNO₃) = 169.8 g/mol; the molar mass of the metal nitrate. M(M) = M(MNO₃) - M(N) - 3 · M(O). Consequently, M(M) = 169.8 g/mol - 14 g/mol - 3 · 16 g/mol, resulting in M(M) = 107.8 g/mol which is the atomic mass of silver (Ag). 3) The balanced chemical equation is: 2AgNO₃(aq) + K₂CrO₄(aq) → Ag₂CrO₄(s) + 2KNO₃(aq). In ionic form: 2Ag⁺(aq) + 2NO₃⁻(aq) + 2K⁺(aq) + CrO₄²⁻(aq) → Ag₂CrO₄(s) + 2K⁺(aq) + 2NO₃⁻(aq). The net ionic equation is: 2Ag⁺(aq) + CrO₄²⁻(aq) → Ag₂CrO₄(s). Thus, the red precipitate is identified as silver chromate (Ag₂CrO₄). 4) The mass of solid silver chromate created is m(Ag₂CrO₄) = 331.8 g. The amount is determined by n(Ag₂CrO₄) = m(Ag₂CrO₄) ÷ M(Ag₂CrO₄). Therefore, n(Ag₂CrO₄) = 331.8 g ÷ 331.8 g/mol yields n(Ag₂CrO₄) = 1 mol. From the balanced equation, n(Ag₂CrO₄): n(AgNO₃) = 1: 2, it follows n(AgNO₃) = 2 · 1 mol, which means n(AgNO₃) = 2 mol. Then, the mass of silver nitrate is computed as m(AgNO₃) = n(AgNO₃) · M(AgNO₃). Hence, m(AgNO₃) = 2 mol · 169.8 g/mol gives m(AgNO₃) = 339.6 g; thus, m(AgNO₄) equals m(K₂CrO₄). Therefore, m(K₂CrO₄) = 339.6 g; amount of potassium chromate is n(K₂CrO₄) = m(K₂CrO₄) ÷ M(K₂CrO₄). Thus, n(K₂CrO₄) = 339.6 g ÷ 194.2 g/mol thus arrives at n(K₂CrO₄) = 1.75 mol. 5) The dissociation of silver nitrate in water is expressed as: AgNO₃(aq) → Ag⁺(aq) + NO₃⁻(aq). Volume of solution a = 500 mL ÷ 1000 mL/L results in V(solution a) = 0.5 L. Concentration equation c(AgNO₃) = n(AgNO₃) ÷ V(solution a), thus c(AgNO₃) = 2 mol ÷ 0.5 L, yielding c(AgNO₃) = 4 mol/L = 4 M. As a result: c(AgNO₃) = c(Ag⁺) = c(NO₃⁻). Thus, c(Ag⁺) = 4 M; the concentration of silver ions in the initial solution a. 6) The dissociation of potassium chromate in water is represented as: K₂CrO₄(aq) → 2K⁺(aq) + CrO₄²⁻(aq). Volume of solution b = 500 mL ÷ 1000 mL/L results in V(solution b) = 0.5 L. Following, c(K₂CrO₄) is calculated as n(K₂CrO₄) ÷ V(solution b). So c(AgNO₃) = 1.75 mol ÷ 0.5 L gives c(AgNO₃) = 3.5 mol/L = 3.5 M. Consequently: c(K⁺) = 7 M; the concentration of potassium ions in solution b. Therefore, c(CrO₄²⁻) = 3.5 M; the concentration of chromium ions in the same solution. 7) The total final volume is V(final solution) = V(solution a) + V(solution b). Thus, V(final solution) = 500.0 mL + 500.0 mL leads to V(final solution) = 1000 mL ÷ 1000 mL/L results in V(final solution) = 1 L. Then n(NO₃⁻) = 2 mol. Therefore, c(NO₃⁻) = n(NO₃⁻) ÷ V(final solution) finds c(NO₃⁻) = 2 mol ÷ 1 L and results in c(NO₃⁻) = 2 M; the concentration of nitrate anions in the final solution. 8) In solution b, there are 3.5 mol of potassium cations while part of that combines with 2 moles of nitrate anions: K⁺(aq) + NO₃⁻(aq) → KNO₃(aq). From the reaction: n(K⁺): n(NO₃⁻) = 1: 1. Thus, Δn(K⁺) = 3.5 mol - 2 mol results in Δn(K⁺) = 1.5 mol, signifying the remaining potassium anions in the final solution. Thus, c(K⁺) = Δn(K⁺) ÷ V(final solution) yields c(K⁺) = 1.5 mol ÷ 1 L, leading to c(K⁺) = 1.5 M; the final concentration of potassium cations.
The temperature difference after 3 hours is 5.16 K. Given that the moles of O₂ inhaled rate at 0.02 mole/min, which converts to 1.2 mole/hour, we know the average heat released during metabolism is 7.2 kJ/h·kg. Therefore, the amount of heat generated within 3 hours will be 7.2 kJ/h·kg multiplied by 3 hours, giving a result of 21.6 kJ/kg, or 21.6 x 10³ J/kg. Applying the formula Qp = Cp x ΔT, and taking the body's heat capacity to be 4.18 J/g·K, we find ΔT = 5.16 K.
