we have a bag that can hold up to 775 ml. we have baking soda and 6 molar of hydrochloric acid. how can we find out how much baking soda and acid we need so that when they react, the gas will fill the bag up just enough so that it wont pop
To find out how much baking soda and hydrochloric acid you need to produce a gas that will fill the bag without causing it to pop, you'll need to consider the balanced chemical equation for the reaction between baking soda (sodium bicarbonate, NaHCO3) and hydrochloric acid (HCl). The reaction equation is as follows:
NaHCO3 + HCl → NaCl + H2O + CO2
From the balanced equation, you can see that one mole of baking soda reacts with one mole of hydrochloric acid to produce one mole of carbon dioxide gas.
Now let's determine the total volume of gas (CO2) that can be accommodated in the bag without causing it to pop.
Step 1: Determine the volume of CO2 at standard temperature and pressure (STP).
- Standard Temperature: 0°C or 273 K (Kelvin)
- Standard Pressure: 1 atmosphere or 101.3 kPa (kilopascal)
- Molar volume (Volume of 1 mole of gas at STP): 22.4 liters
So, at STP, 1 mole (22.4 liters) of CO2 occupies 22.4 liters of volume.
Step 2: Convert the volume of CO2 required into liters.
Since you want to determine the volume in milliliters, convert 775 ml into liters:
775 ml ÷ 1000 = 0.775 liters.
Now, we multiply the required volume (0.775 liters) by the molar volume of CO2 at STP (22.4 liters) to find the number of moles of CO2 needed:
0.775 liters × 1 mole CO2 ÷ 22.4 liters = 0.0346 moles.
Step 3: Calculate the amounts of baking soda (NaHCO3) and hydrochloric acid (HCl) needed.
Since the reaction is 1:1 between the baking soda and hydrochloric acid, you'll need an equal number of moles of each.
Hence, you'll need 0.0346 moles of both baking soda and hydrochloric acid.
Step 4: Calculate the mass of the required amount of baking soda.
Use the molar mass of baking soda to calculate the mass needed. The molar mass of NaHCO3 is:
Na (sodium) = 22.99 g/mol
H (hydrogen) = 1.01 g/mol
C (carbon) = 12.01 g/mol
O (oxygen) = 16.00 g/mol
So, the molar mass of NaHCO3 is:
22.99 + 1.01 + 12.01 + (3 × 16.00) = 84.01 g/mol.
Multiply the molar mass by the number of moles needed:
0.0346 moles × 84.01 g/mol = 2.90 grams (approximately).
Therefore, you'll need approximately 2.90 grams of baking soda.
Similarly, the mass of hydrochloric acid needed is calculated using its molar mass. The molar mass of HCl is 36.46 g/mol.
0.0346 moles × 36.46 g/mol = 1.26 grams (approximately).
Thus, you'll need approximately 1.26 grams of hydrochloric acid (6 molar).
Please note that these calculations assume ideal conditions and may vary slightly depending on factors such as temperature and pressure. It's always best to have appropriate safety measures in place and perform experiments carefully.