the density of H2 gas in a rigid container is 0.117 g/L at 55 C. what is the pressure of hydrogen in the flask if it is heated to 125 C?
1.90
To determine the pressure of hydrogen in the flask when it is heated to 125 °C, you can use the ideal gas law equation:
PV = nRT
Where:
P is the pressure of the gas (in atm)
V is the volume of the gas (in liters)
n is the number of moles of gas
R is the ideal gas constant (0.0821 L·atm/mol·K)
T is the temperature of the gas (in Kelvin)
We can start by converting the temperature from Celsius to Kelvin using the formula:
T(K) = T(C) + 273.15
So, the initial temperature of 55 °C would be:
T1 = 55 °C + 273.15 = 328.15 K
Given that the density of H2 gas is 0.117 g/L, we can use this information to find the number of moles (n) of hydrogen gas using the formula:
density = mass/volume
density = n(Molar mass)/volume
First, let's calculate the molar mass of hydrogen (H2):
Molar mass of hydrogen (H2) = 2g/mol
Now, we can convert the given density into mass (m) per volume (V):
density = 0.117 g/L
Given that the volume is 1 L, we can rearrange the equation to find the mass:
mass = density × volume
mass = 0.117 g/L × 1 L = 0.117 g
Now, we can calculate the number of moles (n) using the formula:
n = mass / molar mass
n = 0.117 g / 2 g/mol = 0.0585 mol
Now we have the initial number of moles (n1), initial temperature (T1), and we need to find the final pressure (P2) at the final temperature (T2).
We can set up a proportion to solve for P2:
(P1 × V1) / (n1 × R × T1) = (P2 × V2) / (n1 × R × T2)
Since the volume (V1) and number of moles (n1) remain constant, we can simplify the equation:
P1 / T1 = P2 / T2
P1 is the initial pressure at T1, V1
T2 is the final temperature of 125 °C converted to Kelvin:
T2 = 125 °C + 273.15 = 398.15 K
Plugging in the values, the equation becomes:
P1 / 328.15 K = P2 / 398.15 K
Now, solving for P2:
P2 = (P1 × T2) / T1
P2 = (P1 × 398.15 K) / 328.15 K
Substitute the given temperature, such as 55 °C:
P2 = (P1 × 398.15 K) / 328.15 K
However, we need to convert °C to Kelvin:
P2 = (P1 × 398.15 K) / 328.15 K
Now you can substitute the initial pressure (P1) and solve for P2.
To solve this problem, we can use the ideal gas law equation, which states:
PV = nRT
Where:
P = Pressure
V = Volume
n = Number of moles of gas
R = Ideal Gas Constant (0.0821 L.atm/mol.K)
T = Temperature in Kelvin
First, let's find the number of moles of hydrogen gas in the container:
To convert the given density to moles per liter, we divide the given density by the molar mass of hydrogen gas (2 g/mol).
Density = 0.117 g/L
Molar mass of H2 = 2 g/mol
Number of moles (n) = Density / Molar mass
n = 0.117 g/L / 2 g/mol
n = 0.0585 mol/L
Now, let's convert temperatures to Kelvin:
Temperature 1 (T1) = 55 °C = 55 + 273 = 328 K
Temperature 2 (T2) = 125 °C = 125 + 273 = 398 K
Now, we can rearrange the ideal gas law equation to solve for pressure:
P1V1 / T1 = P2V2 / T2
Since the volume is constant (rigid container), we can cancel it out:
P1 / T1 = P2 / T2
Now, substitute the given values:
P1 / 328 K = P2 / 398 K
To find P2, we rearrange the equation:
P2 = P1 * (T2 / T1)
P2 = 0.0585 mol/L * 0.0821 L.atm/mol.K * (398 K / 328 K)
Note: The ideal gas constant R is used to convert units to atm.
P2 ≈ 0.072 atm
Therefore, the pressure of hydrogen gas in the flask when heated to 125 °C is approximately 0.072 atm.