We need to find the volume of a balloon that contains 4.4 kg of oxygen at a temperature of 70°C and a pressure of $3.9 \times 10^5$ Pa.

1. Problem Description

We need to find the volume of a balloon that contains 4.4 kg of oxygen at a temperature of 70°C and a pressure of $3.9 \times 10^5$ Pa.

2. Solution Steps

We can use the ideal gas law to solve this problem. The ideal gas law is given by:

$PV = nRT$

Where:

$P$ is the pressure

$V$ is the volume

$n$ is the number of moles

$R$ is the ideal gas constant ($8.314 J/(mol \cdot K)$)

$T$ is the temperature in Kelvin

First, we need to convert the temperature from Celsius to Kelvin:

$T(K) = T(°C) + 273.15$

$T(K) = 70 + 273.15 = 343.15 K$

Next, we need to find the number of moles of oxygen ($O_2$). The molar mass of oxygen is approximately 32 g/mol or 0.032 kg/mol.

$n = \frac{m}{M}$

Where:

$m$ is the mass of oxygen

$M$ is the molar mass of oxygen

$n = \frac{4.4 kg}{0.032 kg/mol} = 137.5 mol$

Now we can plug the values into the ideal gas law and solve for $V$:

$PV = nRT$

$V = \frac{nRT}{P}$

$V = \frac{137.5 mol \times 8.314 J/(mol \cdot K) \times 343.15 K}{3.9 \times 10^5 Pa}$

$V = \frac{392678.8925}{3.9 \times 10^5}$

$V = 1.006868955 m^3$

$V \approx 1.01 m^3$

3. Final Answer

$1.01 m^3$