Question

If a gas occupies 1532.7 mL at standard temperature, what volume does it occupy at 49.4 ºC if the pressure remains constant?

a. 1810
b. 1300
c. 276
d. 3.80e5

Answer 1

a. 1810mL

Step-by-step explanation:

When conditions for a gas change under constant pressure (and the number of molecules doesn't change), it follows Charles' Law:

`(V_1)/(T_1)=(V_2)/(T_2)` where the temperatures must be measured in Kelvin

To convert from Celsius to Kelvin, add 273, or use the equation:
`T_C+273=T_K`

For this problem, one must also recall that standard temperature is 0°C (or 273K).

So,
`T_1 = 273[K]`, and
`T_2 = (49.4+273)[K]=322.4[K]`.

`(V_1)/(T_1)=(V_2)/(T_2)`

`((1532.7[mL]))/((273[K]))=(V_2)/((322.4[K]))`

`\frac{(1532.7[mL])}{(273[K\!\!\!\!\!{-}])}(322.4[K\!\!\!\!\!{-}] )=\frac{V_2}{(322.4[K]\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!{----})}(322.4[K]\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!{----})`

`1810.04571428[mL]=V_2`

Adjusting for significant figures, this gives
`V_2=1810[mL]`