To determine the maximum temperature to which the bulb may be heated without exploding, we need to use the ideal gas law and consider the relationship between pressure, volume, temperature, and the amount of gas.
The ideal gas law is given by:
PV = nRT
Where: P = Pressure V = Volume n = Number of moles of gas R = Ideal gas constant T = Temperature
First, we need to calculate the number of moles of argon gas using its molar mass. The molar mass of argon is approximately 39.95 g/mol.
Number of moles (n) = mass / molar mass n = 0.12 g / 39.95 g/mol n = 0.003004 mol
Next, we need to convert the volume of the bulb from milliliters to liters:
Volume (V) = 150 mL = 0.150 L
Now we can rearrange the ideal gas law to solve for temperature (T):
T = (PV) / (nR)
Substituting the given values:
T = (5.0 atm) * (0.150 L) / (0.003004 mol * 0.0821 L·atm/(mol·K))
Calculating the temperature:
T = 305.76 K
Therefore, the maximum temperature to which the bulb may be heated without exploding is approximately 305.76 K (or approximately 32.61 degrees Celsius).