To solve this problem, we can use the ideal gas law, which states:
PV = nRT
where:
- P is the pressure of the gas
- V is the volume of the gas
- n is the number of moles of gas
- R is the ideal gas constant (0.0821 L·atm/(mol·K))
- T is the temperature in Kelvin
First, we need to convert the given temperatures to Kelvin:
- Initial temperature (27 °C) = 27 + 273.15 = 300.15 K
- Final temperature (-20.0 °C) = -20 + 273.15 = 253.15 K
We can set up the equation using the initial conditions: (700.0 mmHg) * (600.0 mL) = n * (0.0821 L·atm/(mol·K)) * (300.15 K)
Next, we rearrange the equation to solve for n, the number of moles of gas: n = (700.0 mmHg * 600.0 mL) / (0.0821 L·atm/(mol·K) * 300.15 K)
Now we can use the number of moles (n) to find the final volume (V_f) at the given conditions: V_f = (n * R * T_f) / P_f
Substituting the values into the equation: V_f = [(700.0 mmHg * 600.0 mL) / (0.0821 L·atm/(mol·K) * 300.15 K)] * (0.0821 L·atm/(mol·K) * 253.15 K) / 500.0 mmHg
After performing the calculations, the volume of the gas at -20.0 °C and 500.0 mmHg will be determined.