Given the following sets of values for three of the gas variables, calculate the unknown.
P = ? mm Hg; V = 26.0 mL; n = 0.007826 mol; T = 15.6°C
Use PV = nRT and don't forget to change T to kelvin. C + 273 = K.
To calculate the unknown gas variable, we can use the ideal gas law equation:
PV = nRT
Where:
P is the pressure of the gas
V is the volume of the gas
n is the number of moles of the gas
R is the ideal gas constant (0.0821 L·atm/mol·K)
T is the temperature of the gas in Kelvin
First, we need to convert the given temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 15.6°C + 273.15 = 288.75 K
Now we can substitute the given values into the ideal gas law equation and solve for the unknown variable:
P * V = n * R * T
P * 26.0 mL = 0.007826 mol * 0.0821 L·atm/mol·K * 288.75 K
To solve for P, we need to convert the given volume from milliliters to liters:
V(L) = V(mL) / 1000
V(L) = 26.0 mL / 1000 = 0.026 L
Now we can rearrange the equation to solve for P:
P = (n * R * T) / V
P = (0.007826 mol * 0.0821 L·atm/mol·K * 288.75 K) / 0.026 L
By multiplying and dividing, we get:
P = 0.18735 atm
To convert atm to mm Hg, we use the conversion factor:
1 atm = 760 mm Hg
P(mm Hg) = P(atm) * 760
P(mm Hg) = 0.18735 atm * 760
By multiplying, we get:
P = 142.356 mm Hg
Therefore, the unknown gas variable, P, is approximately 142.356 mm Hg.