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a. mass of the ice Step 1: Calculate the heat released by the steam condensing. The heat released by the steam as it condenses into water at 100 °C is given by the formula Q = m · L_v, where m is the mass of the steam and L_v is the latent heat of vaporization of water (2260 J/g). Q_steam = m_steam · L_v Q_steam = 75 g × 2260 J/g Q_steam = 169500 J Step 2: Calculate the mass of the ice using the heat absorbed for melting. The problem states that the heat released by the steam is just sufficient to melt the ice. The heat absorbed by the ice as it melts at 0 °C is given by Q = m · L_f, where m is the mass of the ice and L_f is the latent heat of fusion of ice (334 J/g). Q_ice = m_ice · L_f Since Q_steam = Q_ice: 169500 J = m_ice · 334 J/g m_ice = 169500 J334 J/g m_ice ≈ 507.485 g Rounding to three significant figures: m_ice ≈ 507 g The mass of the ice is 507 g. b. equilibrium temperature of the mixture in the calorimeter Step 3: Identify the components and their initial temperatures after the ice has melted. After the ice has completely melted, the system contains: • Water from condensed steam: m_s = 75 g at 100 °C. • Water from melted ice: m_ice ≈ 507.485 g at 0 °C. These two quantities of water will mix and reach an equilibrium temperature, T_f. The specific heat capacity of water (c_w) is 4.18 J/(g · °C). Step 4: Set up the heat exchange equation. In an insulated calorimeter, the heat lost by the hotter substance equals the heat gained by the colder substance. Q_lost = Q_gained m_s · c_w · (T_initial\_steam\_water - T_f) = m_ice · c_w · (T_f - T_initial\_melted\_ice\_water) 75 g · c_w · (100 °C - T_f) = 507.485 g · c_w · (T_f - 0 °C) The specific heat capacity of water (c_w) cancels out from both sides: 75 · (100 - T_f) = 507.485 · T_f Step 5: Solve for the equilibrium temperature, T_f. 7500 - 75 T_f = 507.485 T_f 7500 = 507.485 T_f + 75 T_f 7500 = (507.485 + 75) T_f 7500 = 582.485 T_f T_f = (7500)/(582.485) T_f ≈ 12.876 °C Rounding to three significant figures: T_f ≈ 12.9 °C The equilibrium temperature of the mixture is 12.9 °C. Send me the next one 📸