ideal gas law calculations (honors only)\n1) what is the ideal gas law formula? what does each variable…

Explanation:

Step1: Recall ideal - gas law formula

The ideal - gas law formula is $PV = nRT$, where $P$ is pressure, $V$ is volume, $n$ is the number of moles, $R$ is the ideal - gas constant, and $T$ is temperature in Kelvin. The value of $R = 0.0821\frac{L\cdot atm}{mol\cdot K}$ when pressure is in atmospheres, volume is in liters, moles are in moles, and temperature is in Kelvin.

Step2: Solve problem 2

Convert units

First, convert the given values to appropriate units.

• $V=890.0\ mL = 0.8900\ L$ (since $1\ L = 1000\ mL$)
• $T=(21.0 + 273.15)\ K=294.15\ K$ (convert Celsius to Kelvin: $T(K)=T(^{\circ}C)+273.15$)
• $P = 750.0\ mmHg=\frac{750.0}{760}\ atm\approx0.9868\ atm$ (since $1\ atm = 760\ mmHg$)
• $R = 0.0821\frac{L\cdot atm}{mol\cdot K}$ From $PV = nRT$, we can solve for $n$: $n=\frac{PV}{RT}$. Substitute the values: $n=\frac{0.9868\ atm\times0.8900\ L}{0.0821\frac{L\cdot atm}{mol\cdot K}\times294.15\ K}\approx0.0364\ mol$

Step3: Solve problem 3

At STP (Standard Temperature and Pressure), $P = 1\ atm$ and $T = 273.15\ K$, $n = 1.27\ mol$, $R = 0.0821\frac{L\cdot atm}{mol\cdot K}$ From $PV = nRT$, we solve for $V$: $V=\frac{nRT}{P}$ Substitute the values: $V=\frac{1.27\ mol\times0.0821\frac{L\cdot atm}{mol\cdot K}\times273.15\ K}{1\ atm}\approx28.5\ L$

Answer:

1. Ideal - gas law formula: $PV = nRT$. $P$: pressure, $V$: volume, $n$: number of moles, $R$: ideal - gas constant, $T$: temperature in Kelvin. $R = 0.0821\frac{L\cdot atm}{mol\cdot K}$
2. $n = 0.0364\ mol$
3. $V = 28.5\ L$