Given an expression relating the Celsius scale and Kelvin scale. Write an expression for the root mean square speed of a gas.

Here are the solutions to the problems. 1. Given an expression relating the Celsius scale and Kelvin scale. Write an expression for the root mean square speed of a gas. Relationship between Celsius and Kelvin scales: The temperature in Kelvin (T_K) is related to the temperature in Celsius (T_C) by the following expression: T_K = T_C + 273.15 Expression for the root mean square (RMS) speed of a gas: The root mean square speed (v_rms) of gas molecules is given by the formula: v_rms = sqrt((3RT)/(M)) where: R is the ideal gas constant (8.314 J mol^-1 K^-1) T is the absolute temperature in Kelvin M is the molar mass of the gas in kg mol^-1 2. Calculate the root mean square speed of hydrogen molecule at 300K (molar mass of hydrogen is 2.016 g/mol, R = 8.314 J mol⁻¹ K⁻¹). Step 1: Identify the given values and convert units if necessary. Temperature, T = 300 K Molar mass of hydrogen (H₂), M = 2.016 g/mol Ideal gas constant, R = 8.314 J mol^-1 K^-1 Convert the molar mass from g/mol to kg/mol: M = 2.016 g/mol × 1 kg1000 g = 0.002016 kg/mol Step 2: Use the formula for root mean square speed. v_rms = sqrt((3RT)/(M)) Step 3: Substitute the values into the formula and calculate. v_rms = sqrt(3 × 8.314 J mol)^-1 K^-1 × 300 K0.002016 kg mol^-1 v_rms = sqrt(7482.6 J mol)^-10.002016 kg mol^-1 Since 1 J = 1 kg m^2 s^-2: v_rms = sqrt(7482.6 kg m)^2 s^-20.002016 kg v_rms = sqrt(3711607.142857 m)^2 s^-2 v_rms ≈ 1926.558 m/s Step 4: Round the answer to an appropriate number of significant figures (e.g., 4 significant figures). v_rms ≈ 1927 m/s The root mean square speed of hydrogen molecules at 300 K is: 1927 m/s