Final answer:
To calculate the pressure in the tube, the Ideal Gas Law is applied after converting the hydrogen gas amount to moles and the temperature to Kelvin. Solving the equation yields the pressure in atm, which can be converted to bar.
Step-by-step explanation:
The question asks to calculate the pressure inside a tube containing hydrogen gas. To find this pressure, the Ideal Gas Law can be used, which is PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature in Kelvin.
Firstly, the amount of hydrogen gas needs to be converted from milligrams to moles. Since the molar mass of hydrogen gas (H2) is approximately 2.016 g/mol, 0.010 mg is 0.010 / 1000 / 2.016 = 4.9603 x 10-9 moles.
Next, the temperature should be converted to Kelvin by adding 273.15 to the Celsius temperature, resulting in 23 + 273.15 = 296.15 K.
Using the Ideal Gas Law, we insert the known values: PV = nRT becomes P(5.0 L) = (4.9603 x 10-9 moles)(0.0821 Latm/molK)(296.15 K). Solving for P gives the pressure in units of atm, which can then be converted to bar (1 atm = 1.01325 bar).