To find the volume of the balloon at standard temperature and pressure (STP) after all the dry ice sublimates, we will follow these steps:
1. Calculate the number of moles of CO2.
2. Apply the ideal gas law to find the volume at STP.
Step 1: Calculate the number of moles of CO2
The number of moles (n) of CO2 can be calculated using the formula:
n = mass / molar mass
Given that the mass of dry ice added to the balloon is 9.00 g and the molar mass of CO2 is 44.01 g/mol, we can calculate the moles of CO2 as follows:
n = mass_dry_ice / molar_mass_CO2
n = 9.00 g / 44.01 g/mol
n ≈ 0.2045 mol
So we have approximately 0.2045 moles of CO2.
Step 2: Apply the ideal gas law to find the volume at STP
The ideal gas law is stated as:
PV = nRT
Where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
At standard temperature and pressure (STP), the pressure (P) is 100 kPa (which is equivalent to 101,325 Pa) and the temperature (T) is 0°C, which is 273.15 K in Kelvin.
Given:
- P = 101325 Pa
- n ≈ 0.2045 mol (from step 1)
- R = 8.314 J/(mol·K) (ideal gas constant)
- T = 273.15 K
We want to find V, so we rearrange the formula to solve for V:
V = nRT / P
Substituting the constants and the value of n we calculated:
V = (0.2045 mol) * (8.314 J/(mol·K)) * (273.15 K) / (101325 Pa)
Now we calculate the volume:
V ≈ (0.2045) * (8.314) * (273.15) / (101325)
V ≈ (463.637535 mol·K·J/(mol·K)) / (101325 Pa)
V ≈ 4.574 m^3
To convert this volume from cubic meters to liters, we use the conversion factor where 1 cubic meter is equivalent to 1000 liters:
V_liters = V_m^3 * 1000 liters/m^3
V_liters ≈ 4.574 * 1000
V_liters ≈ 4574 liters
Therefore, the volume of the balloon at STP after all the dry ice sublimates will be approximately 4574 liters.
