How much water would be needed to completely dissolve 1.64 L of the gas at a pressure of 750 torr and a temperature of 21 C? Henrys law constant is .145 M/atm.
To find out how much water would be needed to completely dissolve 1.64 L of the gas, we can use Henry's law. Henry's law states that the pressure of a gas above a liquid is directly proportional to the concentration of the gas in the liquid.
The formula for Henry's law is:
P = k * C
where:
P is the partial pressure of the gas (in atm),
k is the Henry's law constant (in M/atm), and
C is the concentration of the gas (in Molarity).
In this case, we are given the pressure, temperature, and Henry's law constant, and we need to find the concentration of the gas in order to determine how much water is needed.
First, let's convert the given pressure from torr to atm. Since 1 atm = 760 torr, we can calculate:
Pressure (in atm) = 750 torr / 760 torr/atm = 0.987 atm (approximately).
Next, let's use the ideal gas law to convert the pressure and temperature to moles of gas. The ideal gas law formula is:
PV = nRT
where:
P is the pressure (in atm),
V is the volume of the gas (in liters),
n is the number of moles of gas,
R is the ideal gas constant (0.0821 L·atm/(mol·K)), and
T is the temperature (in Kelvin).
We need to convert the given temperature of 21°C to Kelvin:
Temperature (in K) = 21°C + 273.15 = 294.15 K (approximately).
Now, rearrange the ideal gas law formula to solve for n:
n = PV / RT
Substituting the known values, we get:
n = (0.987 atm * 1.64 L) / (0.0821 L·atm/(mol·K) * 294.15 K) ≈ 0.0542 moles.
The concentration of the gas can be calculated using the volume of the liquid. We know that 1.64 L of the gas is dissolved in a certain amount of water. Assuming the volume of the water is V_water (in liters), the concentration can be written as:
C = n / V_water
We want to find the amount of water (V_water) that would completely dissolve the given amount of gas. So, rearrange the formula:
V_water = n / C
Substituting the known values, we get:
V_water = 0.0542 moles / (.145 M/atm) ≈ 0.374 L (approximately).
Therefore, approximately 0.374 liters (or 374 ml) of water would be needed to completely dissolve 1.64 liters of the gas at a pressure of 750 torr and a temperature of 21°C.