Question

The density of h2 gas in a rigid container is 0.135 g/l at a given temperature. what is the pressure of hydrogen in the flask if it is heated to 201 °c?

Answer 1

The pressure of hydrogen in a flask heated to 201 °C is calculated using the ideal gas law with the provided density to find the number of moles, converting the temperature to Kelvin, and solving for pressure while assuming constant volume and amount of gas.

Step-by-step explanation:

To determine the pressure of hydrogen in a flask when heated to 201 °C, we can use the ideal gas law, PV = nRT, where P is pressure, V is volume, n is number of moles, R is the ideal gas constant, and T is temperature in Kelvin. First, calculate the number of moles of hydrogen gas using its density and the molar mass of hydrogen. The molar mass of H2 is approximately 2 g/mol, so 0.135 g in a liter would mean 0.135 g / 2 g/mol = 0.0675 mol. Convert the temperature from degrees Celsius to Kelvin by adding 273.15 (201 °C + 273.15 = 474.15 K).

Assuming the flask's volume and amount of gas remain constant and recalling R is approximately 0.0821 L·atm/(mol·K), the pressure can then be calculated using the rearranged ideal gas law P = (nRT)/V. Inserting the calculated number of moles, the given volume of 1 liter, and the temperature in Kelvin, you can solve for pressure, P.

Answer 2

Let's assume that H₂ gas has ideal gas behavior.

Then we can use ideal gas formula,
PV = nRT

Where,
P = Pressure of the gas (Pa)
V = Volume of the gas (m³)
n = moles of the gas (mol)
R = Universal gas constant (8.314 J K⁻¹ mol⁻¹)
T = Temperature in Kelvin (K)

But,
n = m/M,
Where m is mass of the gas (kg) and M is molar mass of the gas (kg/mol)

Hence PV= mTR / M
P = mTR / VM = (m/V)TR / M

m/V = d (density (kg/m³)

By rearranging,
P = dRT / M

d = 0.135 g/L = 0.135 kg/m³
T = (273 + 201) K = 474 K
M = 2 g/mol = 2 x 10⁻³ kg/mol

From substitution,
P = 0.135 kg/m³ x 8.314 J K⁻¹ mol⁻¹ x 474 K / 2 x 10⁻³ kg/mol
P = 266006.43 Pa
P = 266 kPa

Hence the pressure of H₂ gas at 201⁰C is 266 kPa