Answer:
[tex]P_1\text{ = 0.434 atm}[/tex]
Explanation:
Here, using the combined gas laws, we want to get the value of the initial pressure
We start by writing the combined gas law formula as follows:
[tex]\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}[/tex]
We have the terms with subscript 1 as initial values while the terms with subscript 2 are final values
Now, let us write out the given values. Kindly understand that the temperature in degrees celsius will be converted to Kelvin by adding 273.15 k to the celsius temperature
We proceed as follows:
[tex]\begin{gathered} P_1\text{ = ?} \\ V_1\text{ = }1.874\text{ L} \\ T_1\text{ = }21.4\text{ + 273.15 = 294.55 K} \\ P_2\text{ = }0.422\text{ atm} \\ V_2\text{ = }2.10\text{ L} \\ T_2\text{ = }47.7\text{ + 273.15 = 320.85 K} \end{gathered}[/tex]
Now, we can rewrite the formula in terms of the missing value before proceeding to substitute as follows:
[tex]P_1\text{ = }\frac{P_2V_2T_1}{V_1T_2}\text{ = }\frac{0.422\times2.1\times294.55}{1.874\times320.85}\text{ = }0.434\text{ atm}[/tex]
