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)
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.
To find the root mean square velocity (v) of molecules of gaseous phosphoric acid (H3PO4) at 158°C, we can use the following equation:
v = sqrt((3 * R * T) / M)
Where:
- v is the root mean square velocity,
- R is the gas constant (8.314 J/(mol·K)),
- T is the temperature in Kelvin, and
- M is the molar mass in kg/mol.
First, we need to convert the temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 158°C + 273.15
T(K) = 431.15 K
Next, we need to calculate the molar mass (M) of H3PO4:
M(H3PO4) = (3 * M(H)) + M(P) + (4 * M(O))
M(H3PO4) = (3 * 1 g/mol) + 31 g/mol + (4 * 16 g/mol)
M(H3PO4) = 3 g/mol + 31 g/mol + 64 g/mol
M(H3PO4) = 98 g/mol
Now, we can substitute the values into the equation:
v = sqrt((3 * R * T) / M)
v = sqrt((3 * 8.314 J/(mol·K) * 431.15 K) / 0.098 kg/mol)
Calculating further:
v = sqrt(10262.1837 J/(mol·K) / 0.098 kg/mol)
v = sqrt(1047078.57 (m^2/s^2)/(kg·mol))
Finally, we take the square root to find the root mean square velocity:
v = 102.33 m/s (rounded to two decimal places)
Therefore, the root mean square velocity of molecules of gaseous phosphoric acid (H3PO4) at 158°C is approximately 102.33 m/s.