Question

a helium balloon has a volume of 10.2 l at -34°c and 366 mm hg. what is its volume at stp?
4.37 l
6.12 l
18.5 l
5.61 l
4.77 l

Explanation:

Step1: Convert temperature to Kelvin

The formula to convert Celsius to Kelvin is \(T(K)=T(^{\circ}C)+273.15\).
For \(T_1=-34^{\circ}C\), \(T_1 = - 34+273.15=239.15K\).
At STP, \(T_2 = 273K\) and \(P_2=760mmHg\).
Given \(V_1 = 10.2L\) and \(P_1 = 366mmHg\).

Step2: Use the combined gas law \(\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}\)

Rearrange for \(V_2\): \(V_2=\frac{P_1V_1T_2}{P_2T_1}\)
Substitute the values:
\(V_2=\frac{366\times10.2\times273}{760\times239.15}\)
First, calculate the numerator: \(366\times10.2\times273=(366\times10.2)\times273 = 3733.2\times273 = 1019163.6\)
Then, calculate the denominator: \(760\times239.15 = 760\times(240 - 0.85)=760\times240-760\times0.85=182400 - 646=181754\)
\(V_2=\frac{1019163.6}{181754}\approx5.61L\)

Answer:

5.61 L