First, we need to calculate the molar mass of H3PO4:
Molar mass of H3PO4 = (3 x molar mass of H) + (1 x molar mass of P) + (4 x molar mass of O)
Molar mass of H3PO4 = (3 x 1 g/mol) + (1 x 31 g/mol) + (4 x 16 g/mol)
Molar mass of H3PO4 = 98 g/mol
Next, we can use the root mean square velocity formula:
u(rms) = √[(3RT)/M]
where:
R = gas constant = 8.31 J/(mol·K)
T = temperature in Kelvin = (158 + 273) K = 431 K
M = molar mass = 98 g/mol
Note: we need to convert the molar mass to kilograms per mole to match the units of the gas constant.
Molar mass in kg/mol = 98 g/mol / 1000 g/kg = 0.098 kg/mol
u(rms) = √[(3 x 8.31 J/(mol·K) x 431 K) / 0.098 kg/mol]
u(rms) = √(11563.53 m²/s²)
u(rms) ≈ 107.5 m/s
Therefore, the root mean square velocity of molecules of gaseous phosphoric acid H3PO4 at 158°C (431 K) is approximately 107.5 m/s.
Find the root mean square velocity of molecules of gaseous phosphoric acid H3PO4 at 158°C. (Molar mass: O= 16 g/mol, H 1 g/mol, P=31 g/mol)
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1 answer