The half-time of the first-order decomposition of nitramide is $2.1$ hour at $15°\mathrm{C}$.

${\mathrm{NH}}_2{\mathrm{NO}}_2 \left(\mathrm{aq}\right)\to {\mathrm{N}}_2\mathrm{O} \left(\mathrm{g}\right)+{\mathrm{H}}_2\mathrm{O} \left(\mathrm{l}\right)$

If $6.2 \mathrm{g}$ of ${\mathrm{NH}}_2{\mathrm{NO}}_2$ is allowed to decompose, calculate the time is taken for $99\%$ decomposition.

The half-time of the first-order decomposition of nitramide is $2.1$ hour at $15°\mathrm{C}$.

${\mathrm{NH}}_2{\mathrm{NO}}_2 \left(\mathrm{aq}\right)\to {\mathrm{N}}_2\mathrm{O} \left(\mathrm{g}\right)+{\mathrm{H}}_2\mathrm{O} \left(\mathrm{l}\right)$

If $6.2 \mathrm{g}$ of ${\mathrm{NH}}_2{\mathrm{NO}}_2$ is allowed to decompose, calculate the volume of dry ${\mathrm{N}}_2\mathrm{O}$ produced (in L) after $99\%$ decomposition at $\mathrm{STP}$.

Answer correct up to one place of decimal.

A toy balloon originally held $1.0 \mathrm{g}$ of helium gas and had a radius of $10.0 \mathrm{cm}$. During the night, $0.25$ $\mathrm{g}$ of the gas effused from the balloon. Assuming ideal gas behaviour under these constant pressure and temperature conditions, what was the radius of the balloon (in cm) the next morning?

Answer correct up to one place of decimal after rounding off.

The escape velocity is given by:

$\mathrm{v}=\sqrt{2\mathrm{gr}}$

where, $\mathrm{r}=6.37\times {10}^6 \mathrm{m}$ for the earth. At what temperature will the $\mathrm{RMS}$ velocity of an ${\mathrm{H}}_2$ molecule attain the escape velocity? The temperature is $\mathrm{a}\times {10}^4 \mathrm{K}.$ Find the value of $\text{'}\mathrm{a}\text{'}$ correct up to two places of decimal.

An $\mathrm{He}$ atom at $25°\mathrm{C}$ is released from the surface of the earth to travel upwards. Assuming that it undergoes no collisions with other molecules, how high will it travel before coming to rest? The height is $\mathrm{a}\times {10}^4 \mathrm{m}$, find the value of $\text{'}\mathrm{a}\text{'}$.