Question

determine the kelvin temperature required for 0.0470 mol of gas to fill a balloon to 1.20 l under 0.998 atm pressure.

Explanation:

Step1: Use ideal gas law

The ideal gas law is \(PV = nRT\), where \(P = 0.998\space atm\), \(V=1.20\space L\), \(n = 0.0470\space mol\), \(R=0.0821\space L\cdot atm/(mol\cdot K)\). We need to solve for \(T\).

Step2: Rearrange the formula

Rearrange \(PV = nRT\) to \(T=\frac{PV}{nR}\).

Step3: Substitute values

Substitute \(P = 0.998\), \(V = 1.20\), \(n = 0.0470\), \(R = 0.0821\) into \(T=\frac{PV}{nR}\).

$$T=\frac{0.998\times1.20}{0.0470\times0.0821}$$

Step4: Calculate

First, calculate the numerator: \(0.998\times1.20 = 1.1976\).
Then, calculate the denominator: \(0.0470\times0.0821=0.0038587\).
Finally, \(T=\frac{1.1976}{0.0038587}\approx310\space K\).

Answer:

\(310\space K\)