Final answer:
To find the pressure of the weather observation balloon at an altitude of 18 km, we can use the ideal gas law equation and the given conditions. By converting the temperature to Kelvin and plugging in the values for pressure, volume, and temperature at ground level, we can find the number of moles of hydrogen. Then, using the number of moles and the conditions at altitude, we can calculate the pressure at 18 km.
Step-by-step explanation:
To solve this problem, we can use the ideal gas law, which states that 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.
First, let's convert the temperature from Celsius to Kelvin. The temperature in Celsius is -50°C, so we add 273.15 to get the temperature in Kelvin: -50 + 273.15 = 223.15 K.
Next, we can use the ideal gas law to find the number of moles of hydrogen. The pressure at ground level is 1 atm, the volume is 30 liters, and the temperature is room temperature, which is approximately 298 K. So we can plug these values into the ideal gas law equation:
(1 atm)(30 L) = n(0.0821 L·atm/(mol·K))(298 K)
Solving for n, we find that there are approximately 1.23 moles of hydrogen.
Finally, we can use the number of moles of hydrogen and the conditions at altitude to find the pressure at 18 km. The pressure at altitude is 0.1 atm and the volume is still 30 liters. So we can again use the ideal gas law equation:
(P)(V) = (n)(R)(T)
(0.1 atm)(30 L) = (1.23 mol)(0.0821 L·atm/(mol·K))(223.15 K)
Solving for P, we find that the pressure at 18 km is approximately 0.065 atm.