This chemistry question involves key chemical concepts and calculations. The detailed solution below walks through each step, from identifying the reaction type to computing the final answer.
ScanSolve AI Answer
Hey Gezahagn, good to see you again. Here are the solutions to the problems: 1. Reaction: CH_4(g) + 2O_2(g) → CO_2(g) + 2H_2O(g) The general rate expression for a reaction aA + bB → cC + dD is given by: Rate = -(1)/(a)([A])/( t) = -(1)/(b)([B])/( t) = (1)/(c)([C])/( t) = (1)/(d)([D])/( t) where the negative sign indicates the disappearance of reactants and the positive sign indicates the formation of products. a) The formation of CO_2 and H_2O Step 1: Write the rate expression for the formation of CO_2. The stoichiometric coefficient for CO_2 is 1. Rate = (1)/(1)[CO_2] t = [CO_2] t Step 2: Write the rate expression for the formation of H_2O. The stoichiometric coefficient for H_2O is 2. Rate = (1)/(2)[H_2O] t b) The disappearance of CH_4 and O_2 Step 1: Write the rate expression for the disappearance of CH_4. The stoichiometric coefficient for CH_4 is 1. Rate = -(1)/(1)[CH_4] t = -[CH_4] t Step 2: Write the rate expression for the disappearance of O_2. The stoichiometric coefficient for O_2 is 2. Rate = -(1)/(2)[O_2] t 2. Reaction: N_2(g) + 3H_2(g) 2NH_3(g) a) The formation of NH_3 Step 1: Write the rate expression for the formation of NH_3. The stoichiometric coefficient for NH_3 is 2. Rate = (1)/(2)[NH_3] t b) The disappearance of N_2 and H_2 Step 1: Write the rate expression for the disappearance of N_2. The stoichiometric coefficient for N_2 is 1. Rate = -(1)/(1)[N_2] t = -[N_2] t Step 2: Write the rate expression for the disappearance of H_2. The stoichiometric coefficient for H_2 is 3. Rate = -(1)/(3)[H_2] t 3. Reaction: 4NO_2(g) + O_2(g) → 2N_2O_5(g) Given: Molecular oxygen is reacting at the rate of 0.037 mol L^-1s^-1. This means -[O_2] t = 0.037 mol L^-1s^-1. From the stoichiometry, the overall reaction rate is Rate = -(1)/(1)[O_2] t = 0.037 mol L^-1s^-1. a) At what rate is N_2O_5 being formed? Step 1: Relate the rate of formation of N_2O_5 to the overall reaction rate. Rate = (1)/(2)[N_2O_5] t Step 2: Calculate the rate of formation of N_2O_5. [N_2O_5] t = 2 × Rate = 2 × 0.037 mol L^-1s^-1 = 0.074 mol L^-1s^-1 b) At what rate is NO_2 reacting? Step 1: Relate the rate of reaction of NO_2 to the overall reaction rate. Rate = -(1)/(4)[NO_2] t Step 2: Calculate the rate of reaction of NO_2. -[NO_2] t = 4 × Rate = 4 × 0.037 mol L^-1s^-1 = 0.148 mol L^-1s^-1 4. Reaction: 4PH_3(g) → P_4(g) + 6H_2(g) Given: Molecular hydrogen is being formed at the rate of 0.078 mol L^-1s^-1. This means [H_2] t = 0.078 mol L^-1s^-1. Step 1: Calculate the overall reaction rate from the rate of formation of H_2. Rate = (1)/(6)[H_2] t = (1)/(6) × 0.078 mol L^-1